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Cài is a Chinese language surname that derives from the name of the ancient Cai state. In 2019 it was the 38th most common surname in China, but the 9th most common in Taiwan (as of 2018), where it is usually romanized as "Tsai" (based on Wade Giles romanization of Standard Mandarin), "Tsay", or "Chai" and the 8th most common in Singapore, where it is usually romanized as "Chua", which is based on its Teochew and Hokkien pronunciation. Koreans use Chinese derived family names and in Korean, Cai is 채 in Hangul, "Chae" in Revised Romanization, It is also a common name in Hong Kong where it is romanized as "Choy", "Choi" or "Tsoi". In Macau, it is spelled as "Choi". In Malaysia, it is romanized as "Choi" from the Cantonese pronunciation, and "Chua" or "Chuah" from the Hokkien or Teochew pronunciation. It is romanized in the Philippines as "Chua" or "Chuah", and in Thailand as "Chuo" (ฉั่ว). Moreover, it is also romanized in Cambodia as either "Chhay" or "Chhor" among people of full Chinese descent living in Cambodia and as “Tjhai”, "Tjoa" or "Chua" in Indonesia.

The Chois are said to be the descendants of the 5th son of King Wen of Zhou, Ji Du. Ji Du was awarded the title of marquis (hóu) of the State of Cai (centered on what is now Shangcai, Zhumadian, Henan, China), and he was known as Cai Shu Du ("Uncle Du of Cai"). Together with Guan Shu and Huo Shu, they were known as the Three Guards. When King Wu died, his son King Cheng was too young and his uncle, the Duke of Zhou, became regent. Seeing that the power of the Duke of Zhou was increasing, the Three Guards got jealous and rebelled against Zhou together with Wu Geng. The Duke of Zhou suppressed the rebellion, and Cai Shu was exiled. King Cheng reestablished Cai Shu's son Wu or Hu as the new Duke of Cai. Some 600 years later in the Warring States period, the State of Chu conquered Cai in 447 BC and was itself conquered by the Qin state which, in turn, formed the Qin Empire, China's first empire. With the spread of family names to all social classes in the new empire, many people of the former state of Cai began to bear it as a surname. The Cai descendants have undertaken the following two major migrations. During the Huang Chao Rebellion (AD 875) at the end of the Tang dynasty (AD 618–907), the Cai clan migrated to Guangdong and Fujian provinces. Another later migration occurred when Ming dynasty loyalist Koxinga moved military officials surnamed Cai and their families to Taiwan in the 17th century. As a result, the surname is far more common in these areas and in areas settled by their descendants (e. g., Southeast Asia) than in other parts of China.

Cai is written the same (蔡) in both simplified and traditional Chinese characters. In Mandarin Chinese, the surname is transliterated as Cài in pinyin and Tongyong Pinyin, Ts'ai in Wade Giles, and Tsay in Gwoyeu Romatzyh. In Southern Min or Taiwanese, it is Chhoà in Pe̍h oē jī. In Cantonese (Hong Kong and Macau), it is Coi3 in Jyutping and Choi in Yale. (This should not be confused with the predominantly Korean family name Choi which has a different character [崔]). In Hakka it is Tshai in Pha̍k fa sṳ. (In Tongyong pinyin, it is Cai in Siyen Hakka and Ca̱i in Hoiliuk Hakka.) In Fuzhou dialect, it is Chái (in Bàng uâ cê).

Koreans use Chinese derived family names and in Korean, Cai is 채 in Hangul, Chae in Revised Romanization, and Ch'ae in McCune Reischauer. Vietnamese also use Chinese derived family names. In Vietnamese, the name is Thái. The Chinese name 蔡 is usually transliterated via Sino Vietnamese as Thái but sometimes as Sái. Japanese do not use Chinese family names but for Chinese in Japan who carry the name, it is さい in Hiragana and Sai in the major romanization systems.

Cai is romanized as Cai in the People's Republic of China, Tsai (or occasionally Tsay or Chai for Mandarin) or Tsoa in Taiwan, and Choi or Choy in Hong Kong and Malaysia. In Malaysia, Singapore, and Brunei, the most common forms are Chua or Chuah for Teochew and Hokkien speakers, Chai for Hakka speakers, Choi or Tsoi for Cantonese speakers, and Toy or Toi for Taishanese speakers. In Indonesia, it is usually romanized as Tjoa/Tjhoa/Tjoea/Tjhoea (Hokkien & Teochew), Tjhoi (Cantonese) or Tjhai (Hakka) with Dutch spelling, or Tjua/Tjhua (Hokkien & Teochew) with old Indonesian spelling, or Chua (Hokkien & Teochew), Choy/Choi (Cantonese) or Chai (Hakka) with current Indonesian spelling. In the Philippines, it is Chua or Cua ( or ). Chua is pronounced in other Anglophone countries outside the Philippines. Other variations include Chye and Coi.

In addition, some of the Chuas (Cais) who resided in the Philippines adopted Spanish names to avoid persecution by the Spanish rulers during the Philippines' Spanish colonial rule from the early 16th to late 19th century. Hispanicized forms of the name include Chuachiaco, Chuakay, Chuapoco, Chuaquico, Chuacuco, Tuazon, Chuateco, and Chuatoco. These names were formed from the surname, one character of the given name, and the suffix " co", a Minnan honorific ko (哥), literally meaning "older brother". so ethnic Chinese formerly surnamed Chua incorporating words that sound like "Chua" and have good meaning (such as Chai, meaning "victory") into much longer surnames. After Suharto came to power, his regime created many anti Chinese legislations in Indonesia. One of them was 127/U/Kep/12/1966 which strongly encouraged ethnic Chinese living in Indonesia to adopt Indonesian sounding names instead of the standard three word or two word Chinese names. Many Indonesianized names are Chinese surname syllables with western or Indonesian prefix or suffix – resulting in many exotic sounding names. Although two Chinese individuals shared the same Chinese surname, they may employ different strategies for the Indonesian sounding names. For example, Indonesianized forms of Cai include Tjuatja, Cuaca, Tjuandi, Cuandi, Tjahjana, Tjahja, etc. Despite the Indonesianization, the Chinese surnames are still used today by the Chinese Indonesian diaspora overseas (mostly in the Netherlands, Germany, and USA); by those Chinese Indonesians courageous enough during Suharto's regime to keep their Chinese names (e. g., Kwik Kian Gie), or by those who couldn't afford to process the name change through Indonesia's civil bureaucracy. After Suharto resigned from the presidency, subsequent governments revoked the ban on the ethnic Chinese from speaking and learning Chinese in public. Using the original Chinese surnames is no longer a taboo but only a small minority have decided to re adopt the original Chinese surnames of their grandparents or to use the Mandarin Chinese pinyin romanization, pronunciation and spelling and most retain their changed names as the post 1965 generations have been culturally Indonesianized.