Artificial neural networks are regarded more and more as universal learning machines, but in some cases, such as when learning the interaction between physical particles it is important to explicitly code into them known invariances, such as invariance to translation, rotation, etc.. The field of group equivariant neural networks has developed to address this challenge. In this talk I will give an overview of this quickly growing field, focusing on its foundations in representation theory, and giving some general prescriptions for building neural architectures that are equivariant to the action of any given compact group. I will demonstrate the methodology with some applications in image recognition, graph learning and force field learning for molecular dynamics.