In this paper, the recent progress of synaptic electronics is reviewed. The basics of biological synaptic plasticity and learning are described. The material properties and electrical switching characteristics of a variety of synaptic devices are discussed, with a focus on the use of synaptic devices for neuromorphic or brain-inspired computing. Performance metrics desirable for large-scale implementations of synaptic devices are illustrated. A review of recent work on targeted computing applications with synaptic devices is presented.