Microservices are a new trend rising fast from the enterprise world. Even though the design principles around microservices have been identified, it is difficult to have a clear view of existing research solutions for architecting microservices. In this paper we apply the systematic mapping study methodology to identify, classify, and evaluate the current state of the art on architecting microservices from the following three perspectives: publication trends, focus of research, and potential for industrial adoption. More specifically, we systematically define a classification framework for categorizing the research on architecting microservices and we rigorously apply it to the 71 selected studies. We synthesize the obtained data and produce a clear overview of the state of the art. This gives a solid basis to plan for future research and applications of architecting microservices.