Photon counting detectors are used in many diverse applications and are well-suited to situations in which a weak signal is present in a relatively benign background. Examples of successful system applications of photon-counting detectors include ladar, bio-aerosol detection, communication, and low-light imaging. A variety of practical photon-counting detectors have been developed employing materials and technologies that cover the waveband from deep ultraviolet (UV) to the near-infrared. However, until recently, photoemissive detectors (photomultiplier tubes (PMTs) and their variants) were the only viable technology for photon-counting in the deep UV region of the spectrum. While PMTs exhibit extremely low dark count rates and large active area, they have other characteristics which make them unsuitable for certain applications. The characteristics and performance limitations of PMTs that prevent their use in some applications include bandwidth limitations, high bias voltages, sensitivity to magnetic fields, low quantum efficiency, large volume and high cost.Recently, DARPA has initiated a program called Deep UV Avalanche Photodiode (DUVAP) to develop semiconductor alternatives to PMTs for use in the deep UV. The higher quantum efficiency of Geiger-mode avalanche photodiode (GM-APD) detectors and the ability to fabricate arrays of individually-addressable detectors will open up new applications in the deep UV. In this paper, we discuss the system design trades that must be considered in order to successfully replace low-dark count, large-area PMTs with high-dark count, small-area GM-APD detectors. We also discuss applications that will be enabled by the successful development of deep UV GM-APD arrays, and we present preliminary performance data for recently fabricated silicon carbide GM-APD arrays.