Tamagawa numbrs and class numbers of algebraic tori were introduced and studied by T. Ono in the 60s, and were investigated by Katayama, Morishita and others. Recently there are progress on computing Tamagawa numbers of Complex multiplication (CM) tori, due to its connections with CM abelian varieties, unitary Shimura varieties and counting abelian varieties over finite fields. In this talk I shall report recent progress on this problem and extensions, based on work of Rued and work in progress with Pei-Xin Liang and Hsin-Yi Yang.