Chen Style Tai Chi {Taiji}while being the original style of Tai Chi is not the only style.

Chen Youben (陳有本; 1780~1858),  of the 14th Chen generation, is credited with starting another Chen training tradition.

This system also based on two routines is known as “Small Frame” (xiao jia; 小架).

Small Frame system of training eventually lead to the formation of two other styles of Tai chi chuan that show strong Chen family influences, Zhaobao style (趙堡架) and Hulei jia (Thunder style; 忽雷架).

However they are not considered a part of the Chen family lineage.

The 4 other main traditional styles are listed below.
Also of note is Cheng Man Ching [a student of yang cheng fu] who created his own simplified yang style and was one of the first Chinese teachers to popularize Tai chi in America, and Feng Zhiqiang who created Hun Yuan Taijiquan.

Hun Yuan t’ai chi ch’uan (Chinese: (traditional) 陳式心意混元太極, (simplified) 陈式心意混元太极) is much like traditional Chen-style Xin Jia with an influence from Shanxi Hsing Yi.
It was created by Feng Zhiqiang 馮志強 (one of Chen Fake’s senior students).
Master Feng, who died on the 5th of May 2012.

“Hun Yuan” refers to the strong emphasis on circular, “orbital” or spiraling internal principles which are at the heart of this evolved Chen tradition.

While such principles already exist in mainstream Chen-style the Hun Yuan tradition develops the theme further.
Its teaching system pays attention to spiraling techniques in both body and limbs and how they may be harmoniously coordinated together.

Specifically, the style synthesizes both Chen tai chi and Xin Yi (both Qigong and, to a lesser degree, martial movements).

Outwardly it appears similar to traditional Old Frame Chen forms and teaches beginners/seniors a 24 open-fist form as well as a 24 Qigong system.

The training syllabus also includes 35 Chen Silk-Reeling and condensed 38 and 48 open-fist forms in addition to Chen Fake’s (modified) Big Frame forms (87 and 73).

YANG STYLE

The Yang family first became involved in the study of Tai chi ch’uan (taijiquan) in the early 19th century.

The founder of the Yang-style was Yang Lu Chan (楊露禪), aka Yang Fu-k’ui (楊福魁, 1799–1872), who studied under Chen Chang Hsing starting in 1820 when he was accepted as the first non Chen family student after 5 generations of Chen Style being kept within the family as a closely guarded secret art.

Yang trained extremely hard and after 18 years in Chen village left to teach in Beijing.

Yang was challenged by many martial arts masters in Beijing and remained undefeated earning him the title at the time as having no equal under heaven and his subsequent expression of t’ai chi ch’uan became known as the Yang-style, and directly led to the development of other three major styles of Tai chi ch’uan (see below). Yang Lu-ch’an (and some would say the art of Tai chi ch’uan, in general) came to prominence as a result of his being hired by the Chinese Imperial family to teach t’ai chi ch’uan to the elite Palace Battalion of the Imperial Guards in 1850, a position he held until his death.

Yang´s grandson Yang Cheng Fu,greatly modified his art making it uniformly slow and steady and more easy for people to practice at any age or physical fitness.

There is no fa~jing ,explosive power releases, jumps, dynamic tempo changes,stamps etc like in Chen Style and most people today

WU STYLE

Wu Chuan-yu (吳全佑, 1834–1902) was a military officer cadet  in the Forbidden City,Beijing and also a hereditary officer of the Imperial Guards Brigade. At that time, Yang Lu Chan (楊露禪, 1799–1872) was the martial arts instructor in the Imperial Guards, teaching Tai chi chuan, and in 1850 Wu Chuan-yu became one of his students.

In 1870, Wu Chuan-yu was asked to become the senior disciple of Yang Pa-hou (楊班侯, 1837-1890), Yang Lu-ch’an’s oldest adult son, and an instructor as well to the Manchu military.

Wu Chuan-yu’s son, Wu Chien-chuan (吳鑑泉, 1870-1942)became the most widely known teacher in his family, and is therefore considered the co-founder of the Wu style by his family and their students.He taught large numbers of people and his refinements to the art more clearly distinguish Wu style from Yang style training

The Wu or Wu (Hao) style (simplified Chinese: 武氏 or 武/郝氏; pinyin: wǔshì or wǔ/hǎoshì) of taijiquan of Wu Yu-Hsiang (武禹襄, 1813-1880), is a separate family style from the more popular Wu Style (吳氏) of Wu Chien- chuan.

Wu Yu-hsiang’s style was third among the five t’ai chi ch’uan families in seniority and is fifth in terms of popularity.

Wu Yu-hsiang was a scholar from a wealthy and influential family who became a senior student (along with his two older brothers Wu Cheng-ching and Wu Ju-ching) of Yang Lu-Chan.

Wu Yu-hsiang wanted to meet the teacher of Yang Lu Chan ,the renowned Chen Master Chen Changxing but as he was in his eighties when Wu visited and no longer teaching new students Chen introduced him to  Chen Qingping,who was a chen master of younger age but very high level gongfu also.

Chen Qingping married a woman from zhaobao so was living there at the time .There are some untrue stories about taiji coming from Chan Sanfeng from wudang,then to zhaobao and from there to chen village.

Actually taiji and bagua also have nothing to do with wudang and have just been practiced there since the 1980´s  The Taiji symbol of yin and yang simply was used by Taoists for over 2,000 years but the martial art of tai chi chuan was created in Chen Village by Chen Wangting around 400 years ago.

Wu´s most famous student was his nephew, Li I -yu(李亦畬, 1832-1892), who  taught Hao Wei-Chen (郝為真, 1842-1920), who taught Li Xiang-yuan, Li Shengduan, Sun Lutang, his son Hao Yeuh -ru (郝月如) and others.

Sun Lutang later on created SUN STYLE Tai Chi. Hao Yüeh-ru in turn taught his son Hao Shaoru (Hǎo Shǎorú, 郝少如) Wu Yu-hsiang’s style of training, so that it is now sometimes known as Wu/Hao or just Hao style t’ai chi ch’uan. Hao Yüeh-ru was teaching in the 1920s, a time when t’ai chi ch’uan was experiencing an initial degree of popularity, and he is known for having smoothed out (in the sense of under-emphasising jumps and snap kicks, etc.) and standardized the forms he learned from his father in order to more effectively teach large numbers of beginners.

Other famous t’ai chi ch’uan teachers, notably Yang Chengfu, Wu Chien-ch’üan and Wu Kung-i made similar modifications to their beginning level forms around the same time.

Wu Yu-hsiang’s t’ai chi ch’uan is a distinctive style with small, subtle movements; highly focused on balance, sensitivity and internal qi development. It is a rare style today, especially compared with the other major styles.

While there are direct descendants of Li I-yü and Li Ch’i-hsüan still teaching in China there are no longer Hao family members teaching the style

Sun Lu-t’ang (1860-1933) was a renowned master of Chinese Neijia (internal) martial arts and was the progenitor of the syncretic art of Sun style taijiquan (孫家). He was also considered an accomplished Neo-confucian and taoist scholar (especially in the I-Ching), and was a distinguished contributor to the theory of internal martial arts through his many published works.

He was born in Hebei and was named Sun Fuquan (孫福全) by his parents. Years later, his Baguazhang teacher Cheng Tinghua (程延華) gave him the name Sun Lutang. (It was common in old China for people to have multiple names).

He continued to use his original name in some areas, including the publishing of his books.

He was also well-versed in two other internal martial art styles: Hsing-i ch’uan and Pa Kua Chang before he came to study Taijiquan. His expertise in these two martial arts were so high that many regarded him as without equal.

Sun learned Wu(Hao) Style Taijiquan from Hao Wei-Chen. Sun started studying with Hao relatively late in his life, but his accomplishments in the other two internal arts led him to develop his t’ai chi abilities to a high standard more quickly than is usual.

He subsequently was invited by Yang Shao-hou, Yang Cheng-Fu and Wu Chien -Chuan to join them on the faculty of the Beijing Physical Education Research Institute where they taught t’ai chi to the public after 1914.

Sun taught there until 1928, a seminal period in the development of modern Yang,Wu and Sun Style Taijiquan.