It has been established experimentally for a long time that the electric charges of the observed particles appear to be quantized. An approach to understanding electric-charge quantization that can be used for gauge theories with explicit U(1) factors-such as the standard model and its variants-is pedagogically reviewed and discussed. This approach uses the allowed invariances of the Lagrangian and their associated anomaly cancellation equations. The authors demonstrate that charge may be dequantized in the three-generation standard model with massless neutrinos, because differences in family-lepton numbers are anomaly free. They also review the relevant experimental limits. Their approach too charge quantization suggests that the minimal standard model should be extended so that family-lepton number differences are explicitly broken. They briefly discuss some candidate extensions (e.g. the minimal standard model augmented by Majorana right-handed neutrinos).