Context: A microservice architecture is composed of a set of small services, each running in its own process and communicating with lightweight mechanisms. Many aspects on architecting with microservices are still unexplored and existing research is still far from being crispy clear. Objective: We aim at identifying, classifying, and evaluating the state of the art on architecting with microservices from the following perspectives: publication trends, focus of research, and potential for industrial adoption. Method: We apply the systematic mapping methodology. We rigorously selected 103 primary studies and we defined and applied a classification framework to them for extracting key information for subsequent analysis. We synthesized the obtained data and produced a clear overview of the state of the art. Results: This work contributes with (i) a classification framework for research studies on architecting with microservices, (ii) a systematic map of current research of the field, (iii) an evaluation of the potential for industrial adoption of research results, and (iv) a discussion of emerging findings and implications for future research. Conclusion: This study provides a solid, rigorous, and replicable picture of the state of the art on architecting with microservices. Its results can benefit both researchers and practitioners of the field.