Collisionless shocks: contemporary state after three quarters of a century of research

The collisionless shock research started in the late 1950s. Since then, plenty of data have been accumulated due to the large number of missions in the heliosphere, providing in situ measurements of the fields and particles. The quality of these measurements has vastly improved, especially in the last two decades. Much more data is available for analysis than is already analyzed. Theoretical studies received a push in 1966, when it was shown that shocks are formed due to the interplay between the nonlinear steepening and dispersive broadening of the magnetic field profile. At present, it is a common point of view that shocks are essentially shaped by the kinetics of ions. So far, we achieved a good semi-quantitative understanding of the ion heating in low-Mach number shocks and the relation of this process to the magnetic profile, and a qualitative understanding of the ion reflection and the nature of the well-structured magnetic field. Rippled and nonstationary quasi-perpendicular shocks have been observed, and theory is being developed.