In this chapter, we will analyze the main mechanisms of self-organization that occur during explosive welding of contacting materials near the interface and thereby ensure adhesion of these materials [82, 83, 89]. When welding is carried out, a number of problems are solved from the very beginning, including the choice of starting materials, the preparation of the surface of the plates for welding, the choice of explosives, the geometry of the explosive impact, etc., which in general allows a certain control over the process of producing a welded joint. In this case, a very significant role is played by the physical characteristics and behaviour of the system of welded plates, to which a large amount of energy is supplied during the explosion. The main part of it, due to the chemical energy of explosives, is the kinetic energy of the flyer plate. The formation of a strong welded joint is most likely possible if the kinetic energy is converted into a change in the internal energy of materials localized near the contact surface. Such a transformation can occur due to various dissipative processes, namely, those that have time to occur in a short time of explosive exposure. These include the formation of different types of cusps on the interface, granulating fragmentation, the adiabatic transition of mechanical energy into thermal energy, melting processes, movement of some defects, etc. At the same time, it can be assumed that from all possible scenarios and methods for implementing this transformation such process is chosen for which the speed of the process, i.e. the rate of conversion of the input mechanical energy into internal energy will be maximum. In particular, the maximum possible should be, first of all, the rate of formation of new boundaries of contacting materials.