The flow of the ground water in an aquifer or during pumping test generates an electrical current (called the streaming current), which is of advective nature. The resulting electrical field (streaming potential field, one of the components of the self-potential field) can be remotely measured at the ground surface or in boreholes. We first discuss the underlying physics of this electrokinetic effect and the role of the electrical double layer coating the surface of the grains. We show how the drag of the excess of electrical charge of the pore water by the flow is equivalent to a source current density. Then, we discuss the metrological aspects, the type of voltmeter and electrodes required to carry out good measurements in field conditions. Two applications are discussed in steady-state conditions. The first is dedicated to the flow of water in shallow aquifers. In this case, the streaming current and the conduction current are nearly balanced and, inside the aquifer, the electrical equipotentials mimic the hydraulic equipotentials. They have, however, the advantage to extend the shape of these hydraulic equipotentials up to the ground surface. The second case is related to the flow of water in the vadose zone, here again investigated in steady-state conditions. In this situation, the vadose zone is polarized and the ground surface electrical potential map reflects essentially the depth of the vadose zone. A case study is shown for a small watershed in the South of France. The resistivity tomography shows no contrast in resistivity between the vadose zone and the aquifer and the observed self-potential data are observed to be linearly correlated to the depth of the water table.