Neuromorphic computing moves beyond the neuronal abstraction adopted by conventional neural networks by taking inspiration from the dynamic, sparse, event-driven signaling and processing exhibited by biological neurons. This talk will first present an overview of the state of the art in neuromorphic computing by focusing on motivation, models, and on the design of training algorithms. This will be done by distinguishing between deterministic and probabilistic models, and by concentrating on principles and intuition. Then, a novel use case for neuromorphic computing in communications will be outlined, namely neuromorphic joint source-channel coding for remote inference over wireless channels. The talk will also offer discussions on the current limitations of the technology and on open problems.