It has been known since Euler that the values of the Riemann zeta function at negative integers are certain rational numbers, namely the Bernoulli numbers Bk. Similarly, the values of Dirichlet L-functions at s=0 are related to class numbers of certain number fields. These are simple instances of a common phenomenon, namely that the values of L-functions at critical points are algebraic, up to a simple factor, and that these algebraic numbers are related to algebraic quantities such as class numbers and Selmer groups. The present talk will be a survey talk on the algebraicity of special values of L-functions and their divisibility properties modulo primes.