Modern simulation techniques have reached a level of maturity, which allows addressing a wide range of problems in chemistry and materials science. Unfortunately, the application of first principles methods with predictive power is still limited to rather small systems, and in spite of the rapid evolution of computer hardware no fundamental change of this situation can be expected. Consequently, to reach an atomic level understanding of complex systems, the development of more efficient but equally reliable atomistic potentials has received considerable attention in recent years. A promising new development has been the introduction of machine learning (ML) methods to describe the atomic interactions. Once trained to electronic structure data, ML potentials can accelerate computer simulations by several orders of magnitude, while quantum mechanical accuracy is preserved. In this article, the methodology of an important class of ML potentials employing artificial neural networks is reviewed.