Buddhism has, at low estimate, 485 Million adherents with high estimates placing it above 530 million, making it the fourth largest religion in the world behind Christianity, Islam, and Hinduism respectively, although if we count irreligion, that is larger. So it's hardly "small". Before the rise of Islam, it was quite possibly the largest religion in the world being the primary religion of parts of India, Southeast Asia, China, Central Asia, Japan, etc. It was the on-and-off state religion of parts of Asia and has been the state religion of Myanmar, Thailand, Śrī Lankā, Cambodia, and Laos, more or less unbroken, for around a thousand years and has remained a major religion in East Asia and mainland Southeast Asia for over a thousand years. So it's pretty significant to them.

But lets get into the nitty gritty. Buddhism was formed about 2,500 years ago in North India by the son of a minor leader of an oligarchic republic based in Nepal. For around 150 years after that the religion was not particularly large and contained to the north parts of the Indian subcontinent into Gandhara (present day East Afghanistan and Pakistan). Then a major king, Aśoka, converts and Buddhism explodes, spreading throughout India, to Śrī Lankā, to the Himalayas, and beyond. It should be said that Aśoka was not simply a Buddhist, but reimagined Buddhist ethics into a secular form, his Dhamma, and did not repress other religions, but rather encouraged respect for all of the Indian religions (he lists Brahmans, Jains, and Ajivikas as well), but his degredation of traditional Brahmanical values led to a Brahmanical backlash where the Brahmans took control and Buddhism began to lose status to a degree in India, especially in the south. However, the Indo-Greeks continued to support Buddhism and helped spread it until the Kushans took control in the early centuries CE where they spread it to China. After the Kushans, Buddhism began a major period of decline in India.

In China and central Asia, Buddhism quickly took hold. Central Asia was quite cosmopolitan at this time and new religions took hold quickly, but China remained somewhat conservative. By the fifth century though, Buddhism had become one of the three main religions in China, initially identifying itself with Daoism, but had become it's own distinct religion. It's flagrant disregard for a number of traditional Confucian values proved a problem for many people in the state, but Buddhism compromised and transformed to accommodate it, and Confucianism and Daoism transformed in turn. Daoism adopted monasticism and systematized it's teachings and Confucianism adopted a cosmology and temples. Not only that, but Buddhism in China became an important political force, with temples gaining economic and political power on their own and through the auspices of rich patrons, including various emperors. This caused periodic state repression, most famously during the T'ang where hundreds of thousands of monks and nuns were disrobed. However, the later T'ang went back on this and supported Buddhism alongside Neo-Confucianism and Daoism. Under the Song, Ch'an (Zen) became the largest religion in their state. The Yuan adopted Sakya Tibetan Buddhism as their state religion, although they ruled a religiously diverse empire, including Manichaeans (who were at this point rather "Buddhacised"), Muslims, and Nestorian Christians alongside the traditional Chinese religions. Buddhism remained a strong political and social force during the Ming, although not to the extent of the Yuan, and then the Qing officially endorsed the Gelug school of Tibetan Buddhism as a way to keep the Mongolians from invading, although Confucianism and Shamanism were the major religions to them. Both the Republic of China and the PRC were officially secular and in the early days of the PRC there was an active effort to destroy Buddhism, it didn't work and there is currently a Buddhist revival in China as well as Taiwan.

But while all of this was going on in China, what was happening to Buddhism in India? Well, like I previously mentioned, Buddhism was entering a period of decline, which you can read more about here in my post, but the long and short of it was that Buddhism was increasingly divorced from the laity and closer to Hinduism. However, Hinduism's absorption of Buddhism was not really one-sided. Advaita Vedanta (and so the now dominant Indian Neo-Vedanta) was founded by Gaudapada, who was deeply influenced by Mahāyāna Buddhist philosophy, especially that of the Mādhyamaka, and interpreted them within the Upaniṣadic framework. His student (or rather the student of his student, but that isn't important), Śankara, systematized and furthered his ideas and came even closer to Buddhism, though he denied it vehemently and there is a strong philisophical difference that is far too complicated to get into here, he even introduced a monastic element to Vedanta which is VERY similar to the Buddhist one. Buddhism remained strong in Bengal and northeast India under the Pālas, where tantrism began and thought continued at the major universities, but the Turkish Muslim invasions spelled the death of Buddhism in India.

However, by this time Buddhism had spread from the Indian subcontinent to Tibet and Indonesia. In the 7th century Songtsen Gampo (srong btsan sgam po), first emperor of Tibet (which then encompassed a major part of Central Asia and China), made an effort to bring Buddhism to Tibet, calling for missionaries from China and India. A century and a half later, Trisong Detsan (khri srong lde btsan) made a much larger effort to bring Buddhism to Tibet and called for two great sages from India; Padmasambhava, a siddha famous for "crazy wisdom", and Śāntarakṣita, a great bhikkhu of the Saravāstivāda school. From China he called for a Ch'an monk, sometimes known as Mahāyāna, but more probably this is a title for the tradition he represented. There were others, but these were the big ones. Tradition holds that there was a debate and that the Indian monks won out and Tibet essentially became a Buddhist nation. Just before the fall of the Tibetan Empire, a king called Langdharma (glang dar ma) repressed, or at least cut support from Buddhism, and was assassinated for it. The next few centuries were dominated by various kings and monks with warring sects, but the Mongols came in and gave rulership of Tibet to the Sakya, and then after the fall of the Yuan, Altai Khan converted to Tibetan Buddhism and with him most of the Mongolian hold-outs and along with the Fifth Dalai lama united Tibet under the Gelug school, who ruled Tibet until 1950. There was absolutely no seperation of church and state to Tibet, to the Tibetans, Buddhism was the government and Tibet was Buddhism (and to a much, much lesser extent Bon, which is more or less indistinguishable from Buddhism outside of very deep philosophy). Much of the later developments of Mahāyāna and Tantra in India are thus preserved in Tibet.

I also mentioned Indonesia. We don't know a heck of a lot about Indonesian (and Malaysian and Philippine) Buddhism since much of it was lost, other than that it was very syncretized with Hinduism. We know that it was spread through economic influence from South India and that it was the state religion of the major maritime empires of the archipelago, but the conversion of major kings to Islam led to a decline of Buddhism and sort of sycretization of Islamic mysticism with Buddhist and Hindu mysticism, which was still there until a large scale reform in the 19th and 20th centuries which is still ongoing to an extent.

Back to China for a sec. From China, Buddhism spread to Japan and Korea where it became a major religion. Korea was essentially a Buddhism country until the Joseon period and in Japan it fused with Shinto and was on and off the major power in Japan. Unlike Shinto, it was organized and had a significant amount of political power, with some temples essentially holding territory and holding a military of their own with abbots being akin to warlords and kings. In the Meiji, Buddhism was repressed and monks defrocked, leading to the idea of "Buddhist priests". After a period of extreme nationalism where many monks were supporting the military to an extreme extent in a bid to remain relevant (this was especially prominent among Zen and Nichiren which both had strong nationalistic elements already), new laity focused Buddhism filled the religious vaccum that opened up after the end of State Shinto and the admission of the Emperor that he was not a god. In Japan today, Buddhist groups like Sokka Gakkai have political wings, some of which are quite successful.

Southeast Asia was dominated by the Hindu Khmer empire for a long time, but around the 11th century they converted to Buddhism. Buddhism first appeared in the mainland from the Pyu and Mon, who appeared to have been a sort of proto-tantra or at least esoteric Buddhism which mixed with the local animism and other forms of worship. In Myanmar, the Pagan Empire, who were a rival to the Khmer, converted large scale and played a vital part in spreading Theravāda throughout mainland SEA. Eventually, the Khmer fell and in their wake a number of kingdoms formed, all of which became Theravāda. Countries quite literally went to war to obtain Buddhist texts and statues, like Thailand and Cambodia appeared to have. Vietnam was largely the exception to all of this since they fell firmly in the Sinosphere and were thus more or less Chinese Buddhists.