The interaction of high-intensity laser pulses with matter releases instantaneously ultra-large currents of highly energetic electrons, leading to the generation of highly-transient, large-amplitude electric and magnetic fields. We report results of recent experiments in which such charge dynamics have been studied by using proton probing techniques able to provide maps of the electrostatic fields with high spatial and temporal resolution. The dynamics of ponderomotive channeling in underdense plasmas have been studied in this way, as also the processes of Debye sheath formation and MeV ion front expansion at the rear of laser-irradiated thin metallic foils. Laser-driven impulsive fields at the surface of solid targets can be applied for energy-selective ion beam focusing.