Microservice API design is a critical aspect in crafting a microservice architecture. While API design in general has been studied, the specific relation of API design to design practices and models commonly used in microservice architectures is yet understudied. In particular, practitioners frequently use Domain-Driven Design (DDD) in their microservice architecture and API designs. We thus decided to study existing Architectural Design Decisions (ADDs), their solutions options, their relations, and the decision drivers in these decisions. Using the Grounded Theory research method we studied grey literature sources. In this study, we identified six ADDs with 27 decision options, numerous relations between them, and 27 decision drivers. The decisions cover mapping domain models to APIs, defining API contracts in relation to domain models, designing API resources based on domain model elements, segregation of API resources, mapping domain model links to the API, and designing the operations of an API resource.

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