Discharges in liquids are very efficient to synthesize nanoparticles by electrode erosion. This simple process is only simple in appearance. Mechanisms responsible for the production of nanoparticles are several depending on the choice of process parameters. They determine size distributions, shapes, composition, and defects of produced particles. They also control their possible assembly into more complex structures. This article describes the basic physics of nanoparticles’ synthesis by discharges in liquids using electrodes and gives a summary of the research efforts that have been devoted to the understanding of this process. A special attention is paid to thermodynamics of these systems driven by discharges that are at or close to local equilibrium. Although a complete picture is not available yet, huge progress has been made and offers new capabilities for a better control of these kinds of processes. Finally, among important challenges that are still to tackle, the possibility of forming nanoalloys from immiscible elements or achieving unimodal monodisperse size distributions is questioned from the current mastery reached in this field