  Atkin and Swinnerton-Dyer congruences are special congruence recursions
satisfied by coefficients of noncongruence modular forms. These are in some
sense $p$-adic analogues of Hecke recursion satisfied by classic Hecke
eigenforms. They actually appeared in different context and sometimes can be
obtained using the theory of formal groups. In this survey paper, we introduce
the Atkin and Swinnerton-Dyer congruences, and discuss some recent progress on
this topic.
