We have presented a novel polarizable electrostatic model that utilizes the direct polarization approximation, typed atomic polarizabilities, and a fast AM1-BCC-dPol charge assignment method. A RESP-inspired model, called RESP-dPol, is also available. Our overall approach is designed to capture the key consequences of electronic polarizability in simulations while remaining convenient to use and computationally tractable. The present results indicate that the polarizable AM1-BCC-dPol model provides a realistic representation of electrostatics at moderate computational cost. Its success may trace in part to the fact that, like some of the most widely used fixed-charge electrostatic models, our model is tuned to replicate gas-phase QM ESPs. Calculations of liquid dielectric constants indicate that the use of a polarizable electrostatic model is crucial to replicate these important experimental observables, for both non-polar and polar liquids.