We present the first x-ray images of electrically exploding wires in air and water, captured at the European X-ray Free-Electron Laser (EuXFEL). These images reveal current shunting in a copper wire during its explosion in air, and the development of electrothermal (and possibly magnetohydrodynamic) instabilities in copper and aluminum wires exploding in water. The experiments were conducted at the Single Particles, Clusters, and Biomolecules and Serial Femtosecond Crystallography instrument (SPB/SFX) at EuXFEL, where fine metallic wires were driven by a pulsed-power generator with a current rise time of ∼1.1 μs and a peak amplitude of ∼28 kA. EuXFEL enabled MHz x-ray radiography of the wires using 20 keV photons and a narrow bandwidth of ∼40 eV. Using the specific current action integral for a copper wire explosion, we provide the first quantitative estimate of the fraction of current that is shunted through the surrounding medium of an exploding wire. Fourier analysis of the electrothermal instability spectrum shows that its wavelength remains mostly independent of the wire diameter once it has exploded, and that the temperature perturbation is similar in magnitude to the average temperature in the wire.