Plasmas heated by lasers have important potential applications, for nuclear fusion and as point-like ultra-short X-ray sources. As the laser beams are very intense and short, the plasma is in a strongly non-equilibrium state. Most notable among its properties are the strongly non-Maxwellian electron energy distribution functions, caused both by the heating itself and by very steep spatial gradients. These non-Maxwellian distribution functions in turn affect strongly the energy transport and the rates of ionization and excitation. Results from one dimensional electron kinetic (Fokker-Planck) numerical simulations of these physical effects will be shown, and some comparisons to experiments. New formulas to correct classical fluid formulations were developed, so that hydrodynamic codes may account for some of this physics without the enormous computation cost of kinetic codes. Similar physical effects also occur in other areas of plasma physics, such as in the diverters of magnetic fusion devices, such as the planned ITER experiment, but with a twist: the time and spatial scales are much longer, but as the density is much lower, the collision times are also longer, so that the dimensionless collisionality is again too small to establish equilibrium. In the future, two dimensional simulations of such non-equilibrium physics will require parallel computing.