This paper presents the topic of context prediction as one possibility to exploit context histories. It lists some expected benefits of context prediction for certain application areas and discusses the associated issues in terms of accuracy, fault tolerance, unobtrusive operation, user acceptance, problem complexity and privacy. After identifying the challenges in context prediction, a first approach is summarized briefly. This approach, when applied to recorded context histories, builds upon three steps of a previously introduced software architecture: feature extraction, classification and prediction. Open issues remain in the areas of prediction accuracy, dealing with limited resources, sharing of context information and user studies.