Motivation of this work is to understand the number of connected components of complex Shimura varieties. We prove an explicit formula for the class number of any CM torus. Consequently, we compute the numbers of CM points as well as connected components of unitary Shimura varieties. One can also use this to count some polarized abelian varieties over finite fields, and the number of connected components of ?classical? Picard modular varieties, namely, the moduli space of n-dimensional principally polarized O_K-abelian varieties, where K is an imaginary quadratic field. This is based on the joint work with Nai-Heng Sheu and Jia-Wei Guo.