Avalanche photodiodes, which operate above the breakdown voltage in Geiger mode connected with avalanche-quenching circuits, can be used to detect single photons and are therefore called singlephoton avalanche diodes SPAD's. Circuit configurations suitable for this operation mode are critically analyzed and their relative merits in photon counting and timing applications are assessed. Simple passive-quenching circuits (PQC's), which are useful for SPAD device testing and selection, have fairly limited application. Suitably designed active-quenching circuits (AQC's) make it possible to exploit the best performance of SPAD's. Thick silicon SPAD's that operate at high voltages (250-450 V) have photon detection efficiency higher than 50% from 540- to 850-nm wavelength and still ~3% at 1064 nm. Thin silicon SPAD's that operate at low voltages (10-50 V) have 45% efficiency at 500 nm, declining to 10% at 830 nm and to as little as 0.1% at 1064 nm. The time resolution achieved in photon timing is 20 ps FWHM with thin SPAD's; it ranges from 350 to 150 ps FWHM with thick SPAD's. The achieved minimum counting dead time and maximum counting rate are 40 ns and 10 Mcps with thick silicon SPAD's, 10 ns and 40 Mcps with thin SPAD's. Germanium and III-V compound semiconductor SPAD's extend the range of photon-counting techniques in the near-infrared region to at least 1600-nm wavelength.