In the ancient Sanskrit language 'ashtau' means the number eight, 'anga' means limbs or branches - 'ashtanga' therefore means something 'eight-branched'. Patanjali refers to the 'eight-fold path' in his definitive work the Yoga Sutra, written around the third century AD. Nowadays the term 'Ashtanga Yoga' is most commonly associated with Ashtanga Vinyasa Yoga, which is a relatively new form, but with some roots and source materials much older.
It was developed from the 1930s onward by yoga guru and Sanskrit scholar, Sri Tirumalai Krishnamacharya. Apparently it is based on an ancient manuscript, the Yoga Kurunta, although there isn't much sound evidence to substantiate this claim. Assisted by one of his top disciples, K. Pattabhi Jois, Krishnamacharya developed a powerful, dynamic, energetic, aerobic form. The style incorporates strong gymnastic influences, uses a powerful breathing technique ('Ujjayi') and links the postures into set sequences with a connecting movement (Vinyasa) resulting in generating deep, detoxifying heat throughout the body.
After Krishnamacharya left Mysore around 1950, K. Pattabhi Jois became the guru of Ashtanga Vinyasa Yoga. Throughout his life Pattabhi Jois claimed that he remained faithful to this form exactly how his guru passed it down to him. Guruji, as he was affectionately called by his students, has devoted all his life to teaching. Until his recent death at the age of 93 he taught at his Yoga Shala in Mysore, South India, and traveled the world to hold workshops.
Through the teachings of K. Pattabhi Jois Ashtanga Vinyasa Yoga spread throughout the world and continues to grow. From the late sixties and early seventies more and more Westerners studied with him, later establishing their own schools in their own home countries. Ashtanga Vinyasa Yoga and many other new dynamic styles developed from it are now taught world-wide, Ashtanga Yoga classes are taught by hundreds of teachers and the style is practiced by many thousands of people.