Neutrino masses provide a direct window into Physics Beyond the Standard Model. It is an open question whether massive neutrinos are Majorana fermions or Dirac fermions. Majorana neutrinos, which violate lepton number conservation, offer an intriguing mechanism for generating small neutrino masses. The most practical experimental approach for discovering Majorana neutrinos is the search for neutrinoless double beta decay. I will present the current results of the EXO-200 experiment, a large liquid xenon detector which is searching for the neutrinoless double beta decay of Xe-136. I will also discuss innovations by the EXO Collaboration and others that will be needed for the next generation of planned detectors and beyond.