Geiger-mode avalanche photodiodes (GMAPDs) are capable of detecting single photons. They can be operated to directly trigger all-digital circuits, so that detection events are digitally counted or time stamped in each pixel. An imager based on an array of GMAPDs therefore has zero readout noise, enabling quantum-limited sensitivity for photon-starved imaging applications. In this review, we discuss devices developed for 3D imaging, wavefront sensing, and passive imaging.