Borrowing a line from an anarchist and mangling it somewhat: happy family members are all alike.  Indeed, the objects of interest of this talk will be families consisting of kindred members having similar characters.  More specifically, I shall present some recent joint work with P. Gao (who visited us in UNSW earlier this year) on the special values of families of $L$-functions.  These include the moments of $L$-functions associated with quadratic and quartic Hecke characters at the central point and the statistics of the low-lying zeros of these same $L$-functions.