The Muon to Electron Conversion (MECO) experiment is designed to detect the coherent conversion of muons to electrons in the field of a nucleus if this process occurs as infrequently as once for 10-17 muons that are captured in a muonic atom. To date, no examples of muon and electron number violating transitions have been seen in charged lepton processes, and MECO will improve the sensitivity of past searches by 3-4 orders of magnitude. MECO has sufficient sensitivity to discover this muon-number violating process if it occurs at rates predicted in several well-motivated models for physics beyond the Standard Model, e.g. a broad class of grand-unified supersymmetric models. I will briefly discuss the motivation for and status of searches for lepton flavor violating (LFV) processes and the status of other experiments under construction, and then describe the MECO experiment. I will concentrate on recent progress on some technical aspects of the experiment and present the prospects for its construction and operation.