This paper summarizes the experience of teaching objectoriented modeling and UML for more than a decade to various audiences (academic or corporate, software developers or not). We present the characteristics of the audiences. We investigate which modeling concepts are well accepted and which are not. We identify a number of general problems: background of attendees, object-oriented language as a prerequisite, limitations of tools, methodological issues, impact of company organizations. We propose (partial) solutions and a list of pragmatic advices. Categories and Subject Descriptors D.2 [Software Engineering]: Miscellaneous General Terms Software Modeling