Risi Kondor University of Chicago & Flatiron Institute Computer Science Deep neural networks have proved to be extremely effective in image recognition, machine translation, and a variety of other data centered engineering tasks. However, generalizing neural networks to learning physical systems requires a careful examination of how they reflect symmetries. In this talk we give an overview of recent developments in the field of covariant/equivariant neural networks. Specifically, we focus on three applications: learning properties of chemical compounds from their molecular structure, image recognition on the sphere, and learning force fields for molecular dynamics. The work presented in this talk was done in collaboration with Brandon Anderson, Zhen Lin, Truong Son Hy, Horace Pan, Erik Thiede and Shubhendu Trivedi.