Nowadays, many companies design and develop their software systems as a set of loosely coupled microservices that communicate via their Application Programming Interfaces (APIs). While the loose coupling improves maintainability, scalability, and fault tolerance, it poses new challenges to the API evolution process. Related works identified communication and integration as major API evolution challenges but did not provide the underlying reasons and research directions to mitigate them. In this paper, we aim to identify microservice API evolution strategies and challenges in practice and gain a broader perspective of their relationships. We conducted 17 semi-structured interviews with developers, architects, and managers in 11 companies and analyzed the interviews with open coding used in grounded theory. In total, we identified six strategies and six challenges for REpresentational State Transfer (REST) and event-driven communication via message brokers. The strategies mainly focus on API backward compatibility, versioning, and close collaboration between teams. The challenges include change impact analysis efforts, ineffective communication of changes, and consumer reliance on outdated versions, leading to API design degradation. We defined two important problems in microservice API evolution resulting from the challenges and their coping strategies: tight organizational coupling and consumer lock-in. To mitigate these two problems, we propose automating the change impact analysis and investigating effective communication of changes as open research directions.