The United Kingdom National Health Service (NHS) maintains guidelines on their website.
It defines Tai Chi as follows:
Tai chi, also called tai chi chuan, combines deep breathing and relaxation with flowing movements. Originally developed as a martial art in 13th-century China, tai chi is now practised around the world as a health-promoting exercise.
It goes on to offer the following view on health benefits:
What are the health benefits of tai chi?
While there's scope for more rigorous research on tai chi's health benefits, studies have shown that it can help people aged 65 and over to reduce stress, improve posture, balance and general mobility, and increase muscle strength in the legs.
The guide goes on to suggest that Tai Chi may provide benefit to some patients with arthritis and those who are at increased risk of falling.
See the full text here - ‘A guide to tai chi’