In the past two decades, machine learning potentials (MLPs) have reached a level of maturity that now enables applications to large-scale atomistic simulations of a wide range of systems in chemistry, physics, and materials science. Different machine learning algorithms have been used with great success in the construction of these MLPs. In this review, we discuss an important group of MLPs relying on artificial neural networks to establish a mapping from the atomic structure to the potential energy. In spite of this common feature, there are important conceptual differences among MLPs, which concern the dimensionality of the systems, the inclusion of long-range electrostatic interactions, global phenomena like nonlocal charge transfer, and the type of descriptor used to represent the atomic structure, which can be either predefined or learnable. A concise overview is given along with a discussion of the open challenges in the field.