In order for solar and visible blind III-nitride based photodetectors to effectively compete with the detective performance of PMT there is a need to develop photodetectors that take advantage of low noise avalanche gain. Furthermore, in certain applications, it is desirable to obtain UV photon counting performance. In this paper, we review the characteristics of III-nitride visible-blind avalanche photodetectors (APDs), and present the state-of-the-art results on photon counting based on the Geiger mode operation of GaN APDs. The devices are fabricated on transparent A1N templates specifically for back-illumination in order to enhance hole-initiated multiplication. The spectral response and Geiger-mode photon counting performance are analyzed under low photon fluxes, with single photon detection capabilities being demonstrated in smaller devices. Other major technical issues associated with the realization of high-quality visible-blind APDs and Geiger mode APDs are also discussed in detail and solutions to the major problems are described where available. Finally, future prospects for improving upon the performance of these devices are outlined.