WignerFamilies generates families of Wigner 3j and 6j symbols by recurrence relation. These exact methods are orders of magnitude more efficient than strategies such as prime factorization for problems which require every non-trivial symbol in a family, and are very useful for large quantum numbers. WignerFamilies is thread-safe and very fast, beating the standard Fortran routine DRC3JJ from SLATEC by a factor of 2-4.