ABSTRACT We study kinetic solutions, including shocks, of initial and boundary value problems for the Euler equations of gases. In particular we consider moving adiabatic boundaries, which may be driven either by a given path or because they are subjected to forces. In the latter case we consider a gas contained in a cylinder which is closed by a piston. Here the boundary represents the piston that suffers forces by the incoming and outgoing gas particles. Moreover, we will study periodic boundary conditions. A kinetic scheme consists of three ingredients: (i) There are periods of free flight of duration τ M , where the gas particles move according to the free transport of equation. (ii) It is assumed that the distribution of the gas particles at the beginning of each of these periods is given by a Maxwellian. (iii) The interaction of gas particles with a boundary is described by a so called extension law, which determines the phase density at the boundary, and provides additionally continuity conditions for the fields at the boundary in order to achieve convergence. The Euler equations result in the limit τ M → 0. We prove rigorous results for these kinetic schemes concerning (i) regularity, (ii) weak conservation laws, (iii) entropy inequality and (iv) continuity conditions for the fields at the boundaries. The study is supplemented by some numerical examples. This approach is by no mean restricted to the Euler equations or to adiabatic boundaries, but it holds also for other hyperbolic systems, namely those that rely on a kinetic formulation.