We present x-ray radiographs of underwater electrically driven exploding copper foils of different thickness, captured at the European X-ray Free-Electron Laser (EuXFEL) using 20 keV (∼30 eV bandwidth) self-amplified spontaneous emission photon beams. The foils were exploded by a ∼30 kA amplitude, ∼1.1 μs rise time current pulse produced by a compact pulsed-power generator. The radiographs reveal rapid frontal expansion of foils accompanied by lateral compression. This occurs due to strong magnetic pressure at the foil edges where, due to lateral skin-effect, the temperature reaches ∼1000 K leading to a fivefold decrease in the yield strength. Furthermore, the explosion begins with the foil edges, consistent with enhanced edge heating due to lateral skin-effect. With relatively thick foils, the bulk of the foil material remains in the liquid phase, and initial longitudinal density non-uniformities, coinciding with the current direction, transform into longitudinal striations. For thinner foils which experience explosion into a plasma, spatially non-uniform density structures appear at the edges of the foil and transverse the current direction. These density modulations, which can be estimated by x-ray attenuation, may be associated with the electrothermal instability (ETI); however, the linear theory of ETI growth does not appear to be applicable at the time of observation.