Theoretical and Experimental Challenges in the Measurement of Neutrino Mass

Neutrino masses are yet unknown. We discuss the present state of effective electron antineutrino mass from β decay experiments; effective Majorana neutrino mass from neutrinoless double-beta decay experiments; neutrino mass squared differences from neutrino oscillation: solar, atmospheric, reactor, and accelerator-based experiments; sum of neutrino masses from cosmological observations. Current experimental challenges in the determination of neutrino masses are briefly discussed. The main focus is devoted to contemporary experiments.