Algebraic subgroups of the Cremona groups

The first results on the tori in the Cremona groups were obtained in the 60s of the last century by A. Bialynicki-Birula. The talk is aimed at describing some later advances in understanding algebraic subgroups of the Cremona groups, including diagonalizable subgroups and triangulable subgroups, and the related problems like the Abhyankar–Sathaye conjecture, and the Bass' question.