This article presents a review of experimental and theoretical studies devoted to the processes that occur during explosions of wires in vacuum when the current densities in the wire are of the order of 108 A/cm2 and the current density rise rates are no less than 1015 A/(cm $^{2}\cdot \text {s}$ ). The theoretical background is focused on the transformation of the wire metal into ionized plasma. In particular, the basic physical notions used to describe wire explosions (WEs; state diagram, current action integral, and metal conductivity changes in phase transitions) are given; magnetohydrodynamic equations are described which are used to simulate WEs, and the simulation predictions are discussed together with their reliability. Extensive experimental data on WEs in vacuum are presented which made it possible to describe the corona and core formation and the development of electrothermal instabilities in the core. The data on the energy deposited in a wire exploding in vacuum reported by different authors are compared. In conclusion, problems are discussed that require additional experimental investigations, namely, the role of metastable states in a WE and the mechanism by which the core is shunted.