Rui or RUI may refer to:
Rui was a Chinese vassal state during the Zhou dynasty (1046–256 BCE).
In 703 BC, the rulers of the five states of Western Guo, Rui, Xun and Jia , and Liang, suppressed Duke Wu of Quwo using armed force.
In 641 BC, the State of Qin easily conquered Rui along with the State of Liang.
Rui is the Mandarin pinyin romanization of the Chinese surname written in Chinese character. It is romanized Jui in Wade–Giles. Rui is listed 209th in the Song dynasty classic text Hundred Family Surnames. It is not among the 300 most common surnames in China.
Rui is a Portuguese first name, also spelled Ruy. It has the same origin as Roderick and Rodrick. People with the given name Rui include:
- Rui Almeida Monteiro (born 1977), Dutch footballer
- Rui Barbosa (1849–1923), Brazilian diplomat, writer, jurist, and politician
- Rui Campos (1922–2002), Brazilian footballer
- Rui Correia (born 1967), Portuguese football goalkeeper
- Rui Costa (born 1972), Portuguese football midfielder
- Rui de Figueiredo (1929–2013), professor, engineer and mathematician
- Rui de Pina (1440–1521), Portuguese chronicler
- Rui Falcão, Brazilian politician
- Rui Faria (born 1979), Portuguese football coach
- Rui Jorge Faria Azevedo (born 1980), Portuguese football goalkeeper
- Rui Alberto Faria da Costa (born 1986), Portuguese cyclist
- Rui Jordão (born 1952), Portuguese football striker
- Rui Jorge (born 1973), Portuguese football back
- Rui Machado (born 1984), Portuguese tennis player
- Rui Nereu (born 1986), Portuguese football goalkeeper
- Rui Patrício (born 1988), Portuguese football goalkeeper
- Rui Rio (born 1957), Portuguese politician and Mayor of Porto (Presidente da Câmara Municipal)