Here are some videos of different systems of Taijiquan. They are presented in order of the school's historical development. Chen Style is the original and oldest system of Taiji. After that Yang system was developed by Yang Lu Chan, followed in order by Wu 武 (Hao) , Wu 吳 and Sun. These videos offer an interesting glimpse into how different Taiji schools prioritize movement concepts and strategies.
Chen Style 陳氏
Yang Style 楊氏
Wu (Hao) Style 武
Wu Style 吳
Sun Style 孫氏
In addition to the classical 5 main systems of Taijiquan listed above, there are other offshoots and modern variations. Here are some of those.
Cannon Fist Forms and Fast Forms
Most people associate the term Taiji (T'ai Chi) only with slow moving forms practice. However, the word Taiji itself means the union of Yin and Yang. In movement, this means the combination of fast and slow. In the oldest system of Taiji, the Chen family system, there are two main empty hand forms, Yi Lu (first form) and Er Lu (second form). Yi Lu is mostly slow, but with faster powerful moved interspersed throughout. Er Lu, also known as the Cannon Fist, is mostly fast with slow moves interspersed throughout. Only this way do we really practice both Yin and Yang together. Only slow is not real Taiji.
Today it is mostly within the Chen system and Chen variants that we see the faster forms still being taught. However, even in other systems that are associated mostly with slow forms (such as Yang family), there are fast forms that were original and integral parts of the systems. Here are some videos of authentic Taiji Cannon Fist or other fast forms.