The training, maintenance, deployment, monitoring, organization and documentation of machine learning (ML) models — in short, model management — is a critical task in virtually all production ML use cases. Wrong model management decisions can lead to poor performance of a ML system and result in high maintenance cost. As research on both infrastructure and algorithms is quickly evolving, there is a lack of understanding of challenges and best practices for ML model management. Therefore, this field is receiving increased attention in recent years, from both the data management and the ML community. In this paper, we discuss a selection of ML use cases, develop an overview over conceptual, engineering, and data-related challenges arising in the management of the corresponding ML models, and point out future research directions.