Photodetectors play a critical role in space lidars designed for scientific investigations from orbit around planetary bodies. The detectors must be highly sensitive due to the long range of measurements and tight constraints on the size, weight, and power of the instrument. The detectors must also be space radiation tolerant over multi-year mission lifetimes with no significant performance degradation. Early space lidars used diode-pumped Nd:YAG lasers with a single beam for range and atmospheric backscattering measurements at 1064 nm or its frequency harmonics. The photodetectors used were single-element photomultiplier tubes and infrared performance-enhanced silicon avalanche photodiodes. Space lidars have advanced to multiple beams for surface topographic mapping and active infrared spectroscopic measurements of atmospheric species and surface composition, which demand increased performance and new capabilities for lidar detectors. Higher sensitivity detectors are required so that multi-beam and multi-wavelength measurements can be performed without increasing the laser and instrument power. Pixelated photodetectors are needed so that a single detector assembly can be used for simultaneous multi-channel measurements. Photon-counting photodetectors are needed for active spectroscopy measurements from short-wave infrared to mid-wave infrared. HgCdTe avalanche photodiode arrays have emerged recently as a promising technology to fill these needs. This paper gives a review of the photodetectors used in past and present lidars and the development and outlook of HgCdTe APD arrays for future space lidars.