The Mandarinterm "t'ai chi ch'uan" literally translates as "supreme ultimate fist" or "boundless fist," or "great extremes boxing". The concept of the "supreme ultimate" appears in both Taoist and Confucian Chinese philosophy where it represents the fusion of Yin and Yang into a single ultimate represented by the Taijitu symbol. The ability to use tai chi as a form of self-defense in combat is said to be the most effective proof of a student's understanding of the art's principles.

The study of tai chi chuan martially is the study of appropriate change in response to outside forces; the study of yielding and blending with outside force rather than attempting to meet it with opposing force. Tai chi classes have become popular in hospitals, clinics, community and senior centers in the last twenty years or so, as baby boomers age and the art's reputation as a low stress training for seniors becomes more well-known. As a result of this popularity, there has been some divergence between those who say they practice tai chi primarily for self-defense, those who practice it for its aesthetic appeal (see wushu below), and those who are more interested in its benefits to physical and mental health. The wushu aspect is primarily for show; the forms taught for those purposes are designed to earn points in competition and are mostly unconcerned with either health maintenance or martial ability. More traditional stylists believe the two aspects of health and martial arts are equally necessary: the yin and yang of tai chi chuan. The tai chi "family" schools therefore still present their teachings in a martial art context whatever the intention of their students in studying the art.
Along with Yoga, tai chi is one of the fastest growing fitness and health maintenance activities in the U.S.