Son of Sirius Black and Hesper Gamp. Regulus had two older siblings: an brother Arcturus (1901-1991) and an sister Lycoris (1904-1965) (BFT). He was not married and had no children (BFT).
This Regulus died just two years before his namesake, Sirius' brother, was born. Although we can't be sure, Regulus probably was a Pureblood and a Slytherin.