The properties of avalanche photodiodes and associated electronics required for photon counting in the Geiger and the sub-Geiger modes are reviewed. When the Geiger mode is used, there are significant improvements reported in overall photon detection efficiencies (approaching 70% at 633 nm), and a timing jitter (under 200 ps) is achieved with passive quenching at high overvoltages (20-30 V). The results obtained by using an active-mode fast quench circuit capable of switching overvoltages as high as 15 V (giving photon detection efficiencies in the 50% range) with a dead time of less than 50 ns are reported. Larger diodes (up to 1 mm in diameter) that are usable in the Geiger mode and that have quantum efficiencies over 80% in the 500-800-nm range are also reported.