Deep neural networks are extremely effective at classic applied machine learning tasks like image recognition, speech, and so on. Generalizing these architectures to learning from structured data such as graphs, however, requires a careful examination of how they handle 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, and Shubhendu Trivedi.