They're Byzantine Catholics who opposed the Monophysites and who were faithful to the Byzantine emperors in their support for the orthodox Christology of Chalcedon (451). Their support of the emperors is evident in their name. Melkite comes from the Arabic word malek or melek, meaning king or emperor.
Originally part of the Greek Schism, the Melkites were reunited with Rome in the 18th century.
Melkites follow the Byzantine rite in Arabic and are illustrative of the Catholic Church's unity within diversity.