This Thesis investigates near infrared ( ~ 1550 nm) time-correlated singlephoton counting, studying the single-photon detectors and some of the potential application areas. Custom designed and fabricated InGaAs/InP single-photon avalanche diode detectors were characterised. Our devices yielded single-photon detection efficiencies of ~10 %, timing jitter of 200 ps, and noise equivalent power comparable to the best commercially available avalanche photodiodes operated in Geiger-mode. The afterpulsing phenomenon which limits the maximum count rate of InGaAs/InP single-photon avalanche diodes has been investigated in detail and activation energies calculated for the traps that cause this problem. This was found to be ~250 meV for all the devices tested, despite their differing structures and growth conditions, and points to the InP multiplication region as the likely location of the traps. Ways of reducing the effects caused by the afterpulsing phenomenon were investigated and sub-Geiger mode operation was studied in detail. This approach enabled freerunning, afterpulsing-free operation at room temperature of an InGaAs/InP singlephoton avalanche diode detector for the first time. Finally, time-of-flight photon counting laser ranging was performed using both singlephoton avalanche diodes and superconducting nanowire single-photon detectors. The use of the latter resulted in a surface to surface depth resolution of 4 mm being achieved at low average laser power at an eye-safe wavelength of 1550 nm.