In the 1970’s, Vera Rubin and her collaborators discovered and established the “Dark Matter Phenomenon”. Despite four decades of intense effort, the nature of Dark Matter remains a major unsolved mystery of particle physics and astrophysics. This talk will highlight some particularly puzzling features and current theoretical, observational and experimental efforts to understand Dark Matter. The Dark Matter Phenomenon also presents a sociological puzzle: why wasn't a Nobel Prize awarded for its discovery? Some background information will be provided, to enable the audience to debate the question.