Density functional theory has been a standard tool in computational materials. Advances in algorithms and computing power continue to increase the complexity and size of systems that can be modeled. There remain many kinds of simulations, however, where DFT is not fast enough to be practical. In Monte Carlo and molecular dynamic simulations, DFT remains too slow to use practically for many systems. Molecular potentials are often used in these applications, but these typically lack the accuracy of DFT, can be difficult to improve and/or validate, have limited utility, and they are difficult to systematically improve. We will discuss the creation, use, and limitations of Behler-Parinello neural networks (BPNN) for materials modeling. We have created and used BPNNs in a variety of systems including carbon, single metals, metal surfaces and adsorbates, alloys and oxides to assess their utility in modeling molecular processes.