The level of penetration of grid-connected photovoltaic (PV) systems has grown very quickly in recent years. Nonetheless, network stresses related to the recurrent voltage and frequency oscillations caused by their irregular power production could be a limiting factor on the future expansion of these applications. With the capability of storing and releasing electrical energy on demand, Energy Storage Devices (ESDs) may play a key role in finding an effective solution to overcome these kinds of problems. The aim of this paper is to provide a description of the state-of-the-art power conversion systems used to combine ESDs and grid-connected PV plants. The work has been edited after an accurate analysis of the current scientific literature, focusing particular attention on medium-high-power PV applications utilizing batteries and/or supercapacitors. A detailed analysis on advantages, disadvantages and range of application is provided for each of the reported conversion systems.