Shock waves are one of the most common plasma phenomena. They play a significant role in astrophysical and magnetospheric environments, as well as in laboratory plasmas. The paper focuses on two issues that underline important similarities and dissimilarities between collisional and collisionless shocks. The two types of shocks are similar in that they can be formed by the overtaking mechanism. We demonstrate that geometrical structures appearing early in the process of shock formation from the generic smooth initial state are quite universal and similar in both cases. Characterization of these structures (dubbed here the 'mussel-shell') is presented. Alongside with these similarities, there exist also significant differences between the two types of shocks. The classical collisional shocks usually connect two well-defined equilibrium states (those before and after the shock transition). Each of these equilibrium states is characterized by the thermodynamic parameters of density, temperature, and pressure whose upstream and downstream values are related by the continuity of mass, momentum, and energy flux. In the collisionless plasmas, however, this description does not work: the final state can be any of the much broader class of states constrained only by the requirement of being stable with respect to collisionless plasma instabilities. To find a final state (which does not have to be Maxwellian) one now has to follow the evolution of the system through the whole transition, and a lot of universality is lost. In some situations even the separation of scales between the global flow and shock transition may be lost. Taken together, these phenomena reveal a fascinating interplay of hydrodynamics, statistical mechanics, and plasma physics.
Electrostatic shock waves in the laboratory and astrophysics: similarities and differences