Many activity processes in space and astrophysical plasmas are closely connected to the existence or formation of current sheets - localized concentrations of the electric current density, which allow fundamental processes such as magnetic reconnection to take place.

To lowest order current sheets can be described as approximately one-dimensional structures and in many cases the spatial variation occurs on kinetic scales. In space plasma collisions can also often be neglected and thus the Vlasov-Maxwell equations have to be used to describe such current sheets.

In this talk I will give an overview of some recent developments in the theory of collisionless current sheets, in particular the search for distribution functions for collisionless force-free current sheet equilibria. I will also show some preliminary results of first studies of their stability properties.