As noted by Walter Reitman, many if not most of the problems tackled by human problem solvers, problems such as composing a fugue, designing a house, or planning a strategy, are ill-defined. But what does it mean for a problem to be ill-defined? Ill-Definedness is an open-textured concept. It does not map automatically to a given situation and the result is often directed by the goals of the author. Prior definitions have focused on the role of constraint propagation in problem solving and the need to justify solutions. Why then the variation and why should we as researchers be concerned? In this talk I will outline prior scholarship in this area.