The field of visible-light continuous time series photometry is now at its golden age, manifested by the continuum of past (CoRoT, Kepler), present (K2), and future (TESS, PLATO) space-based surveys delivering high precision data with a long baseline for a large number of stars. The availability of the high-quality data has enabled astrophysical studies not possible before, including, for example, detailed asteroseismic investigations and the study of the exoplanet census including small planets. This has also allowed to study the minute photometric variability following the orbital motion in stellar binaries and star-planet systems which is the subject of this review. We focus on systems with a main sequence primary and a low-mass secondary, from a small star to a massive planet. The orbital modulations are induced by a combination of gravitational and atmospheric processes, including the beaming effect, tidal ellipsoidal distortion, reflected light, and thermal emission. Therefore, the phase curve shape contains information about the companion’s mass and atmospheric characteristics, making phase curves a useful astrophysical tool. For example, phase curves can be used to detect and measure the mass of short-period low-mass companions orbiting hot fast-rotating stars out of reach of other detection methods. Another interesting application of phase curves is using the orbital phase modulations to look for non-transiting systems, which comprise the majority of stellar binary and star-planet systems. We discuss the science done with phase curves, the first results obtained so far, and the current difficulties and open questions related to this young and evolving subfield.