Wireless networks can be used as platforms for machine learning, taking advantage of the fact that data is often collected at the edges of the network, and also mitigating the latency and privacy concerns that backhauling data to the cloud can entail. This talk will present an overview of some results on distributed learning at the edges of wireless networks, in which machine learning algorithms interact with the physical limitations of the wireless medium. Two topics will be considered: federated learning, in which end-user devices interact with edge devices such as access points to implement joint learning algorithms; and decentralized learning, in which end-user devices learn by interacting in a peer-to-peer fashion without the benefit of an aggregating edge device. Open topics for future research will also be discussed briefly.