The purpose of this article is twofold. First, we review model-based analyses that explore the role of power storage in energy systems with high shares of variable renewables. Second, we introduce a new model that is specifically designed for exploring long-term storage requirements. The literature survey focuses on recent contributions in the peer-reviewed energy economics and engineering literature. We compare key characteristics of the different models, provide an overview of model applications, and summarize key findings on power storage requirements. We also evaluate which system values of storage are covered by respective model analyses. Based on the literature survey, we identify common findings and key model features required for a sound assessment of future storage requirements. In order to raise complementary insights, we introduce DIETER, a new dispatch and investment model. The model contributes to the literature by capturing multiple system values of power storage related to arbitrage, capacity, and reserve provision. Further, the model is designed as an open-source tool that can be freely used and modified. Results of a first application of the new model are presented in a companion paper.