The trend in using games in elementary level education also spreads through higher education levels and specific domains such as engineering. Recently, researchers have shown an increased interest in the usage of games in software engineering. In this paper, we are presenting a systematic review and analysis of 350 papers regarding games in software engineering education that was published in the last fifteen years. After applying our inclusion criteria and manual inspection of these studies, we have ended up with 53 primary papers. Based on a systematic process, we reported and discussed our findings with possible future research directions. The main results of this study indicate that the studies are accumulated around 5 categories: Games that learners/students play, games that learners/students develop as projects, curriculum proposals, developing/coming up with new approaches, tools, frameworks or suggestions and others.