Novel physical functionality enabled by nanoscale control of materials has been the target of intense scientific exploration and interest for the last two decades, leading directly to the explosive growth of nanoscience and nanotechnology. However, this transition to nanometer scales also blurs the boundary between classical physical and electrochemical phenomena, due to smaller transport lengths, larger chemical and electrostatic potential gradients, and higher surface/volume ratios. While well-recognized for many decades in areas such as ferroelectricity, these phenomena remained largely outside the realm of condensed matter physics studies. Here, we offer a perspective on the role of electrochemical phenomena in the nanoscale physics of correlated oxides and summarize the challenges for local characterization of these behaviors.