After initial claims and a long hiatus, it is now established that several binary stars emit high (0.1-100 GeV) and very high energy (>100 GeV) gamma rays. A new class has emerged called gamma-ray binaries, since most of their radiated power is emitted beyond 1 MeV. Accreting X-ray binaries, novae and a colliding wind binary (eta Car) have also been detected - related systems that confirm the ubiquity of particle acceleration in astrophysical sources. Do these systems have anything in common ? What drives their high-energy emission ? How do the processes involved compare to those in other sources of gamma rays: pulsars, active galactic nuclei, supernova remnants ? I review the wealth of observational and theoretical work that have followed these detections, with an emphasis on gamma-ray binaries. I present the current evidence that gamma-ray binaries are driven by rotation-powered pulsars. Binaries are laboratories giving access to different vantage points or physical conditions on a regular timescale as the components revolve on their orbit. I explain the basic ingredients that models of gamma-ray binaries use, the challenges that they currently face, and how they can bring insights into the physics of pulsars. I discuss how gamma-ray emission from microquasars provides a window into the connection between accretion--ejection and acceleration, while eta Car and novae raise new questions on the physics of these objects - or on the theory of diffusive shock acceleration. Indeed, explaining the gamma-ray emission from binaries strains our theories of high-energy astrophysical processes, by testing them on scales and in environments that were generally not foreseen, and this is how these detections are most valuable.
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