Using direct three-dimensional particle-in-cell (PIC) simulations we study the acceleration of electrons and ions in laser–plasma. The PIC simulations allow us to understand the results of actual experiments better, and to look beyond the presently available technology and model for laser parameters that will be obtained in the nearest future. The code VLPL (Virtual Laser-Plasma Laboratory) has been further developed and now it can model the x-ray emission by relativistic electrons in the synchrotron regime. It appears that the strongly non-linear plasma wave excited by a short laser pulse works as a compact high-brightness source of x-ray radiation. We have also checked the possibility of proton trapping in the non-linear plasma wave and find that this is already possible at intensities around 1022 W cm−2.