Electricity systems are expected to experience significant paradigm shifts as the supply moves towards renewable energy. This has the potential to increase demand for flexible resources. This thesis aims to analyze the interactions between energy storage and other power system components in a free electricity market. Various novel models and analysis methods are used to discuss the mechanisms governing these interactions, to analyze the case of storage operating on historic day-ahead market prices, and to inform future modeling efforts. Overall, results highlight the dependence of the systemic impacts and economic value of storage on the system boundary conditions: Its role strongly depends on parameters like residual load patterns and fuel prices. It is paramount to understand the mechanisms behind the system's market-driven operation in order to enable its energy-efficient and cost-efficient development in support of the clean energy transition.