In the context of climate changes and the rapid growth of energy consumption, intermittent renewable energy sources (RES) are being predominantly installed in power systems. It has been largely elucidated that challenges that RES present to the system can be mitigated with energy storage systems (ESS). However, besides providing flexibility to intermittent RES, ESS have other sources of revenue, such as price arbitrage in the markets, balancing services, and reducing the cost of electricity procurement to end consumers. In order to operate the ESS in the most profitable way, it is often necessary to make optimal siting and sizing decisions, and to determine optimal ways for the ESS to participate in a variety of energy and ancillary service markets. As a result, many publications on ESS models with various goals and operating environments are available. This paper aims at presenting the results of these papers in a structured way. A standard ESS model is first outlined, and that is followed by a literature review on operational and investment ESS models at the transmission and distribution levels. Both the price taking and price making models are elaborated on and presented in detail. Based on the examined body of work, the paper is concluded with recommendations for future research paths in the analysis of ESS.