An overview of computational methods to describe high-dimensional potential energy surfaces suitable for atomistic simulations is given. Particular emphasis is put on accuracy, computability, transferability and extensibility of the methods discussed. They include empirical force fields, representations based on reproducing kernels, using permutationally invariant polynomials, neural network-learned representations and combinations thereof. Future directions and potential improvements are discussed primarily from a practical, application-oriented perspective. © 2020 The Author(s).