If you want to know where something is going, it is important to first know where it came from.
The Sankrit word yoga means 'union'. Union of the small, individual self with the whole, infinite and divine self. The path of yoga is a path of union - union of the breath to the body, union of the mind to the muscles, and ultimately union of the creation with the creator. Thus, yoga is not necessarily about achieving the most elegant postures and getting stronger and more flexible. The purpose of yoga at its very essence is to bring about a profound transformation in the practitioner.
Traditional Indian yoga includes both asana (the physical postures that we know today as yoga), breath work, practices of devotion and worship, acts of service, meditation, and chanting. The primary texts of yoga are thousands of years old (the Rig-Veda is the oldest, thought to be written around 1700-1100BC) and asana (the physical poses of yoga) is rarely the primary feature of these texts. In fact, the word asana itself directly translates as 'seat' - a seat for pranayama and meditation, implying that these are the deeper practices in the pursuit of self-realisation.
In 200AD the sage Patanjali wrote his text The Yoga Sutras. This sacred text describes the inner workings of the mind and provides an eightfold path through which we can control the restlessness of the mind and enjoy lasting peace. This eightfold path is now known as Ashtanga which translates as the "eight limbs" of yoga.
Yoga exploded as a means of achieving physical health and fitness in the 1920's, first in India and then in the West. India like much of the world was gripped by an unprecedented fervour for physical activity. This was linked to the struggle for national independence - stronger bodies may lead to a greater capacity to defend the country against colonisers. It was during this period that T. Krishnamacharya (1888-1989) arose and began teaching a very dynamic form of asana practice which was a mash up of early hatha yoga with its deep philosophical and esoterical undertones, wrestling techniques, and gymnastics. He was teacher to the most influential modern teachers including B.K.S. Iyengar, K. Pattabhi Jois, Indra Devi, and T.K.V. Desikachar. Most of the myriad styles of yoga we see in the world today can be directly linked to these teachers.