Current research in interatomic potentials involves using systematically improvable, non-parametric mathematical forms and increasingly complex machine learning methods. The total energy is then written V T O T = ∑ ∑ i N E ( q i ) where q i is a mathematical representation of the atomic environment surrounding the atom i , known as the descriptor. E is a machine-learning model that provides a prediction for the energy of atom i based on the descriptor output. An accurate machine-learning potential requires both a robust descriptor and a suitable machine learning framework. The simplest descriptor is the set of interatomic distances from atom i to its neighbours, yielding a machine-learned pair potential. However, more complex many-body descriptors are needed to produce highly accurate potentials. It is also possible to use a linear combination of multiple descriptors with associated machine-learning models. Potentials have been constructed using a variety of machine-learning methods, descriptors, and mappings, including neural networks, Gaussian process regression, and linear regression.