Bhutan's National Olympic Committee was formed in 1983 and was recognized by the International Olympic Committee within that same year. They then joined the Summer Games for the first time in 1984 which was held in Los Angeles, California, USA.
Bhutan's national sport is archery which is why it is not that surprising that their Olympic athletes have been exclusively made up of archers. From 1984 Los Angeles Games all the way to the 2008 Beijing Olympics, Bhutan only participated in one sport.
In 2012 however, they first had a non-archer in the team. Kunzang Choden represented Bhutan in the women's 10 meter air-rifle competition. Bhutan has never sent that many athletes to the Summer Games which is why it is not quite a surprise that they are yet to take home an Olympic medal. For years, archery has been their make or break sport and they are yet to "make" it.
Despite being one of the most mountainous countries in the world, Bhutan has never joined the Winter Games.