The growing maturity of integrated photonic technology makes it possible to build increasingly large and complex photonic circuits on the surface of a chip. Today, most of these circuits are designed for a specific application, but the increase in complexity has introduced a generation of photonic circuits that can be programmed using software for a wide variety of functions through a mesh of on-chip waveguides, tunable beam couplers and optical phase shifters. Here we discuss the state of this emerging technology, including recent developments in photonic building blocks and circuit architectures, as well as electronic control and programming strategies. We cover possible applications in linear matrix operations, quantum information processing and microwave photonics, and examine how these generic chips can accelerate the development of future photonic circuits by providing a higher-level platform for prototyping novel optical functionalities without the need for custom chip fabrication. The current state of programmable photonic integrated circuits is discussed, including recent developments in their building blocks, circuit architectures, electronic control and programming strategies, as well as different application spaces.