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 can result in high maintenance cost. As both research on infrastructure as well as on 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, both from the data management as well as from the ML community. In this paper, we discuss a selection of ML use cases, develop an overview over conceptual, engineering, and data-processing related challenges arising in the management of the corresponding ML models, and point out future research directions.