The present work reviews the results, obtained by numerical examination of the space and time behavior of ion charges in electrolytic cell when external electric field is applied. The basic governing equations for free ions have been generalized for ion-pairs, the simple boundary conditions for blocking electrodes are generalized taking into account the charge transfer currents at the electrodes, the equilibrium Einstein-Nernst relation between ion mobility and diffusivity is modified to take into account the transient, non-equilibrium processes. All these problems are tackled with the help of a common numerical algorithm applied in both linear and nonlinear approximation. Special attention is attributed to nonlinear processes, to thin cells with nano-scaled inter-electrode gap, to non-equilibrium states and their relaxation to equilibrium, to the enhancement of the interface electrode polarization and capacity by charge pump through a complementary electrode etc. Recent patents concerning electrochemical cells and super-capacitors have also been shortly reviewed.