We present a brief overview of current developments in the field of polymer electrolytes, with the focus on single-ion conducting polymers. The latter have significant advantages relative to electrolytes with dual-ion conductivity for use in energy storage devices. First we discuss various mechanisms of ionic conductivity in polymers and fundamental limitations imposed by these mechanisms. We also emphasize the role of ion-ion correlations in conductivity that are not negligible in concentrated and semidilute ionic systems. Next we discuss several classes of polymer electrolytes (gels, block copolymers, and composites) that are already employed or have good potential to be employed in current battery technologies. At the end we discuss perspectives for the design of dry single-ion conducting polymer electrolytes with required room temperature conductivity.