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Modeling is an essential and challenging activity in any engineering environment. It implies some hard-to-train skills such as abstraction and communication. Teachers, project leaders, and tool vendors have a hard time teaching or training their students, co-workers, or users. Gamification refers to the exploitation of gaming mechanisms for serious purposes, like promoting behavioral changes, soliciting participation and engagement in activities, etc. We investigate the introduction of gaming mechanisms in modeling tasks with the primary goal of supporting learning/training. The result has been the realization of a gamified modeling environment named PapyGame. In this article, we present the approach adopted for PapyGame implementation, the details on the gamification elements involved, and the derived conceptual architecture required for applying gamification in any modeling environment. Moreover, to demonstrate the benefits of using PapyGame for learning/training modeling, a set of user experience evaluations have been conducted. Correspondingly, we report the obtained results together with a set of future challenges we consider as critical to make gamified modeling a more effective education/training approach.