He is a member of the Social Democratic Party, and was previously the Estonian Minister of Culture 1995–1999 (Estonian: Eesti kultuuriminister).

Allik studied at the University of Tartu with a bachelor's degree in philosophy and a major in sociology and history, later working as a lecturer in that same university.

Because Allik had been a part of the Estonian Communist Party since 1971 (and, ultimately, the CPSU), he became part of groups such as the Supreme Soviet and involved with notable Estonian communists such as Mikk Titma and Indrek Toome.

His maternal half-sister is the sociologist and politician Marju Lauristin.

His son, Mihkel Allik, has been an advisor to the Chancellor of Justice.