In hydrothermal systems associated with volcanic areas, the flow of groundwater generates an electrical current of electrokinetic nature, the so-called streaming current. This current is associated with the drag of the excess of charge located near the surface of the minerals, in the liquid pore water, in the so-called Gouy-Chapman diffuse layer. In turn, the streaming current generates an electrical field (the streaming potential) that can be remotely recorded at the ground surface of the Earth (or in wells) with a simple voltmeter and pairs of non-polarizing electrodes. A map of self-potential signals can be obtained at any scale using some specific procedures to correct for the drifting of the electrodes or error closures in the mapping of these signals at large scales (tens of kilometers). We first review the underlying physics of self-potential signals. Then we discuss forward and inverse modeling with specific examples pertaining to volcanic areas. Several case studies of large scale self-potential anomalies are discussed. We show how self-potential signals can be used to assess the pattern of groundwater flow in such hydrothermal systems. In addition, we discuss how transient hydro-mechanical disturbances can generate transient self-potential anomalies than can be, in turn, inverted to obtain information on the source of these signals including their localization and magnitude. The next grand challenge to monitor active volcanoes will be the combination of transient self-potential signals with time-lapse electrical conductivity and induced polarization tomography and hydromechanical simulation codes.