Well, for starters, Bhutan was invaded. I can confirm at least eight attempts at invading Bhutan by her neighbors. Seven by Tibet (armed with Mongol hordes) and once by Britain.

Bhutan traditionally obtained independence in 1616 with the scion of the Drukpa Kagyu branch of Buddhism - the Zhabdrung Ngawang Namgyal - left Tibet and settled in the south. Bhutan - then called Lhomon - was not a centralized state and we can confirm quite a bit of archeological evidence and some scattered rule here and there, but the Zhabdrung set out to create what we would otherwise call a State in the seventeenth century. I describe quite a bit of this on the AskHistorians Podcast here.

The long story short is that the political situation in Tibet changed during this process and the Zhabdrung initially thought the situation could be solved when the Fifth Dalai Lama came to power in 1642. Instead, the Fifth sided with his own cousin (with whome the Zhabdrung had been quarelling) and launched invasions of Bhutan. All in all, there were seven of them. Only the last was mildly successful, occurring in the early 1700s, well after both the Zhabdrung and the Great Fifth had been dead and their successors stopped pretending they were alive.

This last invasion (c.1730 if I remember correctly) occurred under the Tibetan man-who-would-be-king Polhanas (Po-lHa-ney) who gave up trying to conquer Bhutan and settled for what was essentially a large raid, demanding tribute from the Bhutanese Desi (Regent) and declaring victory back in Tibet. These invasions were all led by Tibetans, but once the Dalai Lama got involved, he was allied and backed up pretty much entirely with Mongol military power, so the armies were hybrids, made up of Tibetans and Mongols.

Bhutan was mostly at war with itself until the mid-1800s. By then Britain was conquering India and doing a good job of it, and was looking A. for more places to plant tea, B. for more access to China (just in case), and C. to stop the pesky Bhutanese from raiding into their territory which they had just conquered from the Assamese, but which formed an essential part of the Bhutanese economy.

Bhutan was ruled at that time by "the Black Regent," Jigme Namgyal, the great-great-great-grandfather of the current 5th King Jigme Khesar Namgyal Wangchuck. Jigme Namgyal was a savvy politician, and saw how the British angled their way into Sikkim earlier, and how they conquered the Assamese. When the British came to enforce an uneven treaty on them through Sir Ashley Eden, he played on Eden's misunderstanding of their culture and inability to speak the language and purposely humiliated the man. Eden returned to India referring to the Bhutanese as barbarians who won't understand anything but force.

So in 1864, the British invaded Bhutan. They had an easy time going in, but a very difficult time getting out. Jigme Namgyal wouldn't let his forces face the British directly, and chose a campaign of guerilla warfare. The British could conquer Bhutan, but they couldn't hold it. In 1865, the Treaty of Punakha was signed which solidified Bhutan's southern border with India (basically handing over a lot of Bhutanese land, called the "Duars" or "Doors" to British rule, hence the war is often referred to as "the Duar War"), and stopping Bhutanese raids into British held territory so long as the British paid a yearly stipend to the Bhutanese in compensation.

And while a lot of history has happened since then, this treaty (or more accurately, the clauses in it which have been inherited through other treaties) is still in effeect. The Republic of India has confirmed and upheld the treaty, and the rupees paid to the Bhutanese have gone up over time with inflation and form a vital part of the Bhutanese economy. Bhutan was never invaded by China because that would trigger a war with India, and India never invaded because... well why would they? The Bhutanese upheld their part of the bargain and are probably India's closest ally (there are Indian military bases in Bhutan).