The propagation of laser-generated hot electrons through matter and across narrow vacuum gaps is studied. We use the ATLAS titanium–sapphire laser of Max-Planck-Institut für Quantenoptik to irradiate aluminum and copper foils at intensities of up to 1019 W/cm2, generating electrons with temperatures in the megaelectron volt range. After propagating through the target the electrons are detected by means of visible Čerenkov radiation generated in a dielectric or hard X-rays emitted from an X-ray “fluor.” These diagnostics allow the electrons to be characterized with respect to their energy, number, and directionality. We also investigate the propagation of the hot electrons across narrow vacuum gaps, with a width ranging from 500 μm down to 50 μm. The effect of self-generated fields in preventing electrons from crossing the gap is demonstrated. Implications of these experiments with respect to fast ignitor physics, developing optics for fourth-generation light sources and X-ray lasers are indicated.