Development of numerical methods for hydraulic fracture simulation has accelerated in the past two decades. Recent advances in hydraulic fracture modeling and simulation are driven by increased industry and research activity in oil and gas, a drive toward consideration of more complex behaviors associated with layered and naturally-fractured rock formations, and a deepening understanding of the underlying mathematical model and its intrinsic challenges. Here we review the basic approaches being employed. Some of these comprise enhancements of classical methods, while others are imported from other fields of mechanics but are completely new in their application to hydraulic fracturing. After a description of the intrinsic challenges associated with the mechanics of fluid-driven fractures, we discuss both continuum and meso-scales numerical methods as well as engineering models which typically make use of additional assumptions to reduce computational cost. We pay particular attention to the verification and validation of numerical models, which is increasingly enabled by an ever-expanding library of laboratory experiments and analytical solutions for simple geometries in a number of different propagation regimes. A number of challenges remain and are amplified with a drive toward fully-coupled, three-dimensional hydraulic fracture modeling that accounts for host-rock heterogeneity. In the context of such a drive to complex models, we argue that the importance of best-practice development that includes careful verification and validation is vital to ensure progress is constrained by the appropriate underlying physics and mathematics with a constant attention to identifying conditions under which simpler models suffice for the intended modeling purposes.