Ultraviolet (UV) studies in astronomy, cosmology, planetary studies, biological and medical applications often require precision detection of faint objects and in many cases require photon-counting detection. We present an overview of two approaches for achieving photon counting in the UV. The first approach involves UV enhancement of photon-counting silicon detectors, including electron multiplying charge-coupled devices and avalanche photodiodes. The approach used here employs molecular beam epitaxy for delta doping and superlattice doping for surface passivation and high UV quantum efficiency. Additional UV enhancements include antireflection (AR) and solar-blind UV bandpass coatings prepared by atomic layer deposition. Quantum efficiency (QE) measurements show QE > 50% in the 100-300 nm range for detectors with simple AR coatings, and QE ≌ 80% at ~206 nm has been shown when more complex AR coatings are used. The second approach is based on avalanche photodiodes in III-nitride materials with high QE and intrinsic solar blindness.