Energy storage systems are pivotal for maximising the utilisation of renewable energy sources for smart grid and microgrid systems. Among the ongoing advancements in energy storage systems, the power conditioning systems for energy storage systems represent an area that can be significantly improved by using advanced power electronics converter designs and control techniques. Normally, the battery, flywheel, ultracapacitor and superconducting magnetic energy storage are the types of energy storage systems that typically require power conditioning systems for efficient bidirectional power flows. Compared to the previous review papers, this paper critically reviews the power conditioning system configurations and control techniques from the perspective of energy storage system applications in the power systems. First, the power conditioning systems are categorised into DC bus power conditioning systems and AC bus power conditioning systems based on the output voltage types at the connected point. Next, the topologies and control configurations of popular power electronics are comparatively analysed to highlight their advantages and power system applications. Moreover, the control configurations are discussed in terms of the popular applications of energy storage systems, that is, power backup smoothing, frequency regulation, voltage regulation and power quality applications. In addition, the latest developments in the energy storage system such as multi-functional energy storage system stacking, artificial intelligence for power conditioning system of energy storage systems and security of control of energy storage systems are critically analysed. Finally, the review is concluded by discussing industrial applications and future research trends for the power conditioning systems of energy storage systems.