Ionic motion and electrochemistry in bulk materials and at their surfaces have long been studied for their relevance in several areas of science and technology, ranging from ionic conductors to batteries to fuel cells. The ability to engineer materials at the nanometer scale, however, has made these concepts even more relevant. This is due to the large surface-to-volume ratios typical of nanostructures. This implies, for instance, that chemical reactivity and defect motion at surfaces or interfaces are enhanced or may be fundamentally different compared to their bulk counterparts. In addition, nominally modest voltages or differences in chemical potential when applied across nanoscale distances can produce large electric fields and diffusive forces. While all of this may complicate the interpretation of experimental results, it also presents us with new opportunities for materials engineering. In this article, we will briefly review the current research status of several systems where ionic motion and electrochemical effects are of particular importance. These include resistive switching systems, oxide heterostructures, ferroelectric materials, and ionic liquids. We will report on experimental results and also emphasize open questions regarding their interpretation. We will conclude by discussing future research directions in the field.