Edit: Please read this excellent comment by WaylonWillie, below, before reading any further in my current comment tree. WaylonWillie presents a much more succinct and panoramic response that actually answers the call of OP's question (Sino-Tibetan relations in bullet point form).

(Original text of my post below - exercise caution, as I started off too far back in the historical record, progressed in too much detail, and ran out of steam well before I could get to the more salient parts of the more recent history. I'm still new to this.)

Wolfram Eberhard is a good source for a precis of Chinese history. His accessible A History of China is available for free online (and also on Kindle) and it tends to focus on economic pressures for the activity of the metropolitan Chinese kingdoms and outlying tribes. It specifically explodes and debunks the popular portrayal of "China as a great civilization surrounded by barbarians" and instead shows China as a nation surrounded by and interacting with numerous peripheral peoples who were nevertheless quite developed, and these interactions were both constructive and antagonistic at times, with the flow of benefit going in both directions.

Eberhard also avoids the simplistic view that "Chinese", "Tibetan", "Mongol" etc. were monolithic, unchanging, clearly-traceable ethnicities or nations throughout history - when in reality they shifted in geographic location, cultural identity, ethnic makeup, and languages and customs.

A summary of the context of Eberhard's earliest mentions mentions of Tibet in his text:

• The current Tibetans were likely descended from an ancestral people who lived around Gansu, Sichuan, Shaanxi (although no mention of Tibet/Xizang and Qinghai?) who were likely hillside sheep herders. (Perhaps distinguishing them from the agricultural center and the horse-breeding tribes of the northern plains, e.g. the precursors to the Xiongnu.) Circa 2500 BCE. (Chapter 1, Section 5)

• Tibetan artifacts from around this time include painted pottery, which apparently tied Tibetan culture more closely with Turkic culture and remains found as far west as the Danube. (Though Eberhard specifically admits the evidentiary gaps of contemporary East Chinese pottery archaeology.) This painted pottery was a primary source of evidence about the Xia dynasty, of which practically no written script remains. Thus, the Xia dynasty made widespread use of a pottery form that spread to them from the proto-Tibetan culture to the west. (Ch.1 §6)

• The first "historical" dynasty, the Shang (the first period of which we have durable writing - in the form of oracle bones) had elements of Tibetan, Mongol, and Turkish culture. (Ch.2 §1) However, the Shang dynasty was also "in more or less a continuous state of war" with "Qiang tribes, belonging to the Tibetan culture" (Ch.2 §1) The Shang dynasty dates approximately from 1600 BCE to 1028 BCE.

Thus far, according to Eberhard, we see cultural crossovers as early as the Xia dynasty in its pottery as far as 4500 years ago, and then a state of recorded warfare from about 3600 years ago. Note, however, that Eberhard doesn't identify Tibetans as a specific national polity or single tribe - it's merely a cultural group, to which various tribes can be classified. Apparently Shang-era China was influenced by Tibetan culture, yet clashed constantly with peripheral tribes that also identified with Tibetan culture.

Moving on in the text:

• The successor Zhou dynasty (1028 - 257 BCE) brought in traits that Eberhard identifies as being "culturally Chinese" (such as a strong patriarchy, feudal elements, and a shift away from agrarian fertility religion to the later Chinese traditional religion). This tribe originated from Shaanxi, again a periphery province, and containing many Turkic and Tibetan influences, and it established a military rule with garrisons forming the primary urban centers, expressed through feudal tributaries. (Ch.3 §1)

• Later assimilation between Zhou and conquered Shang brought the landed ruling houses in conflict with their outlying, semi-nomadic peoples of Turks, Mongols, and Tibetans. (Ch.3 §3) Eberhard clearly rejects the standard historical view: the outlying tribes were not just violent barbarians who waged war or raided the metropolitan center just for the love of it - they were the indigenous herders displaced by the expanding garrisons and the crowds of artisans and peasants relocated to serve these garrison towns. As the herders' own subsistence agriculture grew less efficient, it became more cost-effective to simply barter or raid for their agricultural goods. "This abandonment of agriculture brought them into a precarious situation: if for any reason the Chinese stopped supplying or demanded excessive barter payment, the nomads had to go hungry. They were then virtually driven to get what they needed by raiding." (Ch.3, §3)

The above elements set the stage for the context of Sino-Tibetan relations up until the present. Key departures from the standard narrative are: 1) "Tibetan" is not a specific defined tribe or ethnicity, as much as a cultural category that dates back to an extremely ancient root. 2) "Chinese", according to Eberhard, is an even more amorphous and variable term, given the huge amount of cultural influx, economic shifts, and ethnological change. My own personal reading of the term is that it generally refers to a mostly geographical category, of landed metropolitan agricultural-intensive provinces and its surrounding hinterlands or coast (much as the Chinese term Zhongguo 中国 literally means "central state"). 3) The interplay between Chinese and Tibetan throughout history is complex and cannot be simply represented as universally hostile, as various actors within each group had very different relations and the two sides were not monolithic.

Tibet and China have had both productive and antagnoistic relations for centuries. Rich historical evidence dates from the Tang dynasty (so, saying they have had relations "forever" perhaps plays into the claim you sometimes see in contemporary Chinese media that Tibet has "always" been a part of China).

Standard introductory sources on Tibet/China relations would be Goldstein, Snow Lion and the Dragon (a short work, but his massive histories are recommended if you get into it); Tsering Shakya, Dragon in the Land of Snows; Blondeau (ed.), Authenticating Tibet. You might enjoy the last one, as it is a series of short, digestible essays by reliable scholars on critical issues in Tibet / China relations, and also addresses politicized presentations of Tibetan culture and religion.

You ask for a series of bullet points on Tibet / China relations. The topic gets very nuanced, and sometimes can be misunderstood if you leave out the details. But with that said, here is a short list leaving out the details, but trying to be careful (it is a Saturday morning and I am not fully in scholarly mode):

• From 650 to 850 (speaking in very round numbers) the Tibetan empire is militaristic and expansionistic, capturing territories from its neighbors, attacking Chinese prefectures, and causing instability along China's western borders. In 763, Tibet famously attacks the Tang dynasty capital of Chang'an, and briefly occupies it. Tibet during this period is clearly not "a part of China" and is not subject to Chinese military or administrative control.

• Following the collapse of the Tang, little substantial political contact (that would be included in a bullet point list) until....

• Yuan Dynasty: both China and Tibet are overtaken by the Mongolian empire that establishes the Yuan Dyanasty in China. The process of Tibet submitting to the Mongolians happens generally between 1240-1260. Kublai Khan formally establishes the Yuan Dynasty in China, 1271. This is a major turning point: Tibet is clearly administered by a political entity based in China. (Does that make sense? Tibet submitting to the Mongolian empire that also conquers China is different than "China invading Tibet".)

• Following the decline of the Yuan, "Chinese" control of Tibet fades. There is a series of short-lived dynasties in Central Tibet (in very rough terms, let's say, from 1350-1600). There is plenty of strife and sectarian warfare here, which may be different from what your Buddhist teachers teach you!

• In 1642, the 5th Dalai Lama "unifies" central Tibet, backed by the military might of the Mongolian Gushri Khan.

• Turmoil in the century after the 1682 death of the 5th Dalai Lama. In the 1720s, interested in stability, the Qing Dynasty allies itself with the youthful 7th Dalai Lama (who is not yet enthroned), escorts him to central Tibet, and supports his enthronement. Here again we have Tibet coming under the power of a political entity based in China. (Does this make sense? The Qing was another "foreign" dynasty in China, i.e. established by non-ethnically Chinese. I'm not trying to belabor this point, as "Tibet" is clearly back under the control of "China" here, but it is significant.) From this period until the 20th century, the Qing has what Goldstein calls a "passive hegemony" over Tibet. Administrators are present in Tibet, they are interested in preventing Tibet from being invaded or from being subject to massive internal conflict, but Tibetans can exercise political control, as long as they operate within those boundaries.

• In the early 20th century, the British invade Tibet, reaching Lhasa in 1904. Wanting to reestablish more firm control, the Qing invades, and the 13th DL flees into exile. In a stroke of luck for Tibet, the Qing falls in 1912. The 13th DL returns to Lhasa, and expels all foreign administrators.

• During the ensuing period, 1913-1933, there are no Chinese officials in Tibet, and no Chinese control. This is often referred to as Tibet's "de facto" independence.

• In 1949, Mao establishes the modern PRC, resulting in the modern situation you probably know about. In 1950 China's army easily takes the Tibetan town of Chamdo, and is poised to march into Lhasa. To prevent certain military defeat of its capital, a Tibetan delegation signs the 17 point agreement in 1951 (without the explicit permission of the Dalai Lama). This document formally makes Tibet a part of China. In 1959 there is an uprising in Lhasa, resulting in massive violence as the Chinese army tries to quell it. The DL flees to exile and the Tibetan government ends (this also ends the 17 point agreement).

• According to Chinese political sources, following that time, Tibetans were liberated from the oppression of their religious feudal government, and currently enjoy lives of incredible wealth and happiness, loudly singing the praises of the Motherland. (Be sure to check on this last one.)

I suggest you read a few books on Tibetan History for the details. The Story of Tibet by Thomas Laird with consultation by the Dalai Lama is fraught with issues, but is a good view into the Tibetan perspective of the situation. So don't stop there, read The Secret Lives of the Dalai Lama by Alexander Norman which is a little more academic treatment of the subject. You can start branching out from there. Histories of China take a peripheral view of the subject often categorizing Tibet as barbarians in a similar view to the Mongols and Turkic tribes of the north. I love The History of Bhutan by Karma Phuntsho which is sort of the reverse: a peripheral view of Tibet from her southern neighbor Bhutan, which is a very interesting read when it comes to the Tibeto-Chinese narrative. I don't have my library and I'm supposed to be grading papers, so you can start with those books and let the adventure into Tibetan history begin.

But the bullet points on the Tibeto-Chinese relationship:

• 600s, tribes now referred to as the Qiang migrate from the Yangtze Valley onto the Tibetan Plateau. This is probably very true and the beginning of China's claim to modern Tibet: "Well, the Tibetans started off as Chinese any way, so we're just bringing them back into the fold." The Qiang, however, were mostly illiterate and probably left because they were previously considered a minority group, pastoralists and nomads looked down upon by the settled agricultural Chinese.

• 700 and 800s, the Tibetan Empire (referred to often as Tufan) is built by the Yarlung Dynasty. They build a castle on the hill that Potala Palace is currently located on. The first of the "Great Buddhist Kings" marries a dozen or so Tibetan women and then seeks to expand his empire. Tibet is a super power in the region, expanding south into the Bengal, north into the Tarim Basin, and east into China. Songtsen Gampo, the first "GBK" also marries a Nepalese Princess and a Chinese Princess, most of the world considers this normal diplomatic practice (think feudal Europe), modern China claims that Princess Wencheng's marriage to the Tibetan Emperor was a sign of submission to China (but not a sign of submission to Nepal, curiously. The Emperor is almost always portrayed either alone or with both of his wives. Chinese commentaries on these images talk extensively of Princess Wencheng, but never of Princess Bhikruti). The lasting significance of the marriages is that both Princess Bhikruti and Princess Wencheng are the first to bring Buddhism to Tibet. The former brings the Indian variety called Vajrayana, the latter brings Chinese Ch'an.

• This "forever antagonism" is a bit of a tunnel vision on the historical reality. Tibet and China were only two contenders for control over the Silk Road. The aforementioned Turko-Mongol tribes, expanding Arab and Muslim forces from the west, and probably a few other forces I'm forgetting fought for control over the Gansu Corridor and the Tarim Basin with Yarlung Tibet and T'ang China.

• The first of the other two Great Buddhist Kings - Trisong Detsen and Tri Ralpachan - actually invaded and sacked Xi'an, the capital of T'ang China. Tibet occupied China briefly before signing a treaty. This is the height of the Tibetan Empire. I believe there are still pillars standing in the PRC written in Chinese and Tibetan where they regard each other as equals and affirm peace for "The Tibetans in Tibet and the Chinese in China." Tibetans are pretty big on these pillars as a sign of their opppression.

• Trisong Detsen invited an Indian Prince-turn-Monk named Padmasambhava (called Guru Rinpoche, or "Precious Teacher" in Tibetan) to Tibet to teach the religion. He did so and all Buddhism in Tibet is descended from Guru Rinpoche. However, at the time Bodhidharma and Princess Wencheng's effects were still felt in Tibet. Vajrayana - Buddhism of the Indian variety - and Ch'an - the Chinese variety - competed fiercely (for a time with also Muslim, Christian, and Manichaean competition) for royal support. Under Trisong Detsen, two Buddhist monks held an epic debate over which school of Buddhism would become the state religion of Tibet. Mo He Yan, the Ch'an proponent lost to the Indian Vajrayana monk Kamalasila. Reportedly, Trisong Detsen named Kamalasila the winner because Vajrayana held more emphasis on morality than Ch'an.

• Tri Ralpachan was assassinated (allegedly) by his brother Lang Darma who was sponsored by the Bön (Tibet's indigenous religion) faction in his court. Buddhism took a hit in the country for a time (it's debated at how big of a hit) and the Emperor was assassinated by a Buddhist monk in a ritual tantric killing. Without an heir, the Tibetan Empire fell apart into a series of petty states on the Plateau. There was no state support for Buddhism and what little survived became the Nyingma school.

• After the T'ang there was no force powerful enough to send military or political missions from China to the Plateau. The Song Dynasty - despite being powerful and a bastion of Chinese culture and technology - was mostly confined to the coastal provinces. Most of the area the PRC claims would actually be taken over by otherwise "barbarian" tribes. The Song would retreat far to the south of the Yellow River as the Jurchen conquered northern China and various Tibetan tribes would vie for control of petty kingdoms on the Plateau. The aforementioned Gansu Corridor would be taken over by the Tangut tribe, who the Chinese now refer to as the Western Xia and claim as their own. The most evidence we have, however, points to the Western Xia as being a Tibetan tribe.

• In this era of petty states and confusion there was a second dissemination of Buddhism that tempered the effects of the first one. The Muslims were rampaging through India destroying as many idols and scriptures as they could. Thanks to Indian (especially Bengali) teachers coming to Tibet, there was a renewed Tibetan interest in Buddhism and many spiritual seekers went to India, translated many scriptures, and took them back to Tibet with them. Tibetan Buddhism is what remains of the dead Bengali form propagated by the Pala Dynasty.

• The Mongols. The Tangut submitted to Chinggis Khaan and then rebelled. This was one of the Seven Cardinal Sins for the Mongols (the first would be killing the messenger). The Tangut were... well, annihilated so thoroughly there was a long period of history where historians believed they were as fictional as Atlanteans (hence why we have so little information). Anyway, the Tibetans submitted to the Mongols in 1241 to Doorda Khaan. In 1271, Qhubilai Khaan established the Yuan Dynasty in China. Tibet, China, and Mongolia were administered separately, but the Mongol Khaans became fat, decadent, and sinicized. The Chinese today claim the Yuan Khaans as their own as proof of their sovereignty over Tibet.

• The Mongols were very religiously tolerant. It was a pragmatic endeavor: they ruled an empire with Muslims, Buddhists, Christians, Confucians, Taoists, shamans, animists, etc. etc. so it was just easier to let them all worship their own gods and pray for the Khaan's health all the same. Surely one of them must be right? As the Mongol Empire went on, however, they became less tolerant. One of the Mongol princes asked a Tibetan lama to come to China and teach Buddhism. The lama, Phagspa, the hierarch of the Sakya school of Tibetan Buddhism was given control as Prince-Lama of Tibet. He was also asked to come to the capital in the east to (long story short) hold a debate with Taoist Priests. Qhubilai declared Phagspa the winner of said debate and it was the beginning of a favorable relationship with the Mongols and Tibetans.

• When the Mongols were overthrown in China with the rise of the Ming, Tibet also revolted. There's some contention over how much control the Ming had over Tibet. What the histories seem to show is that, sure, the Ming claimed control over the Plateau as the more or less "official successors" of the Yuan, they held very little actual control over the Plateau. The Sakya Prince-King successors to