Mobility prediction is a powerful tool for network operators to optimize network performance. From cell level, if network operators know the cells to which the users will be connected in advance, wireless resources can be pre-allocated to improve network performance and better user experience can be provided in location-based services. Many next-cell prediction models and methods have been suggested and implemented. This paper is devoted to next-cell prediction (cell level mobility prediction) in cellular networks, and provides a thorough survey of the prediction schemes and applications. Particularly, a two-level classification methodology was proposed and applied. We first divided the prediction schemes into three categories based on the mobility data used for prediction, i.e. Current Movement State based Approaches (CMSA), Historical Movement Pattern based Approaches (HMPA), and HybriD Approaches (HDA). Prediction schemes in each category were further classified based on the used prediction methods. The typical application scenarios were introduced as well, including handover management, resource allocation, etc. Finally, current challenges and potential trends in the near future were further discussed.