Single photon avalanche diodes (SPADs) are revolutionizing ultra-sensitive photodetection applications, providing single photon sensitivity, high quantum efficiency and low dark noise at or near room temperature. When aggregated into arrays, these devices have demonstrated the ability to operate as photon number resolving detectors with wide dynamic range, or as single-photon imaging detectors. SPAD array performance has reached a point where replacing vacuum tube based MCP and PMT photodetectors for most applications is inevitable. Compound semiconductor SPAD arrays offer the unique proposition to tailor performance to match application specific wavelength, speed and radiation hardness requirements. We present a theoretical framework describing performance limits to compound semiconductor SPAD arrays and our latest experimental results detailing the performance of GaAs SPAD arrays. These devices achieve nanosecond rise and fall times, excellent photon number resolving capability, and low dark count rates. Single photon number resolving is demonstrated with 4% single photon detection efficiency at room temperature with dark count rates below 7 Mcps/mm2. Compound semiconductor SPAD arrays have the opportunity to provide orders of magnitude improvement in dark count rate and radiation hardness over silicon SPAD arrays, as well as the ability to detect wavelengths where silicon is blind.