Krishnamacharya can be credited as "the father of modern yoga". The origins of yoga itself are obscure in ancient history and are estimated as being somewhere between 4,000 and 8,000 years ago, but it is clear that until Krishnamacharya's era (1888 to 1989 CE) yoga was practiced mainly by a small group of ascetics who tended to live in caves, removed from society. Krishnamacharya might be considered as the yogi who broke yoga into the mainstream, all the while shying away from fame and fortune.
Krishnamacharya taught all of the key figures in modern-day yoga, including T.K.V. Desikachar (his son), the late Indra Devi, Pattabhi Jois (the founder of Ashtanga yoga), B.K.S. Iyengar (founder of Iyengar yoga). Much mystery commonly remains about yoga, but the core of Krishnamacharya's system is simplicity itself once understood. He taught that yoga itself was divided into six broad tools (or krama, in Sanskrit):

• Srsti - "growth"; suitable for the young, mainly focused on developing strengh, flexibility and power.
• Siksana - "perfection".
• Raksana - "maintenance"; suitable for adults.
• Adhmatya - "spiritual matters".
• Cikitsa - "healing" or "therapy".
• Sakti or Shakti - "energy"; the most abstract, esoteric and mystical parts of yoga, to do with spiritual transcendence. Only ever practiced by a few "elite" yogis (noting that elitism is not a yogic concept).
In the West, most popular yoga teaching is heavily focused on asana practice, which is just one of the "eight limbs" of yoga, as defined by Patanjali. However to focus so strongly on fixed regimes of asana is not a fair representation of Krishnamacharya's yoga. In Krishnamacharya's system, only Srsti, Siksana and Cikitsa were focused on asana, with the other three kramas sharing equal importance. Krishnamacharya taught yoga as a blended balance between all six kramas, and it is said that he became the teacher each student needed, rather than resorting to rigid repetition of set sequences (such as in Ashtanga yoga, which is derived from Krishnamacharya's book Yoga Makaranda) or focusing only on physical perfection and alignment (such as in Iyengar yoga).
Modern forms of yoga can be analysed in terms of the six kramas. The asana sequences of Ashtanga yoga, with their heavy aerobic focus, can be considered Srsti, but also Raksana once mastered. The heat produced by Ujayyi breath during an Ashtanga session causes sweat, which is said to purify the body; this can be considered Cikitsa. Iyengar yoga, with its avoidance of vinyasa and focus on alignment is more based on Siksana and Raksana and not so much Srsti. Pranayama is Adhmatya, with elements of Cikitsa and Sakti.
Yoga overall is one of the six classical schools of Indian philosophy, Samkhya, Nyaya, Vaisheshika, Purva Mimamsa and Vedanta, and draws heavily on Samkhya, the oldest of the six. Krishnamacharya studied all six philosophies, achieving preeminence in everything that he studied. His approach to teaching yoga was therefore shaped by his knowledge of all of them, as well as Ayurveda and astrology.
 

It is said that Krishnamacharya drew upon all of these bodies of knowledge to become the teacher that each student needed. Notably, he rarely taught in groups, and the famous students of his listed above all studied under him individually. A clear distinction between Krishnamacharya's approach and the more strongly-branded systems can be seen.