STARRY computes light curves for various applications in astronomy: transits and secondary eclipses of exoplanets, light curves of eclipsing binaries, rotational phase curves of exoplanets, light curves of planet-planet and planet-moon occultations, and more. By modeling celestial body surface maps as sums of spherical harmonics, STARRY does all this analytically and is therefore fast, stable, and differentiable. Coded in C++ but wrapped in Python, STARRY is easy to install and use.