Some metals share an elusive property with silicon (and other semiconductors): they may exhibit strong self-induced current oscillations during anodic dissolution in electrochemical experiments. While this feature, as well as related features concerning self-organization at reactive solid-liquid interfaces, is still not well understood, the so-called "current-burst model" of the authors succeeded.in reproducing many effects quantitatively that have been observed at the Si electrode. The current-burst model assumes that current flow through the electrode on a nm scale is inhomogeneous in both time and space; a single current-burst is a stochastic event. Current oscillations in time and space result from interactions in space or time of single currentbursts. The paper outlines the basics of the model and gives results of Monte Carlo simulations concerning stable and damped oscillations for the current and, as a new feature, for the voltage. With the current-burst model a kind of "nano"-electrocheniistry is introduced; its strengths, weaknesses, and possible implications for other electrochemical phenomena and for other materials are briefly discussed.