X-ray lasers bring us into a new world in photon science by delivering extraordinarily intense beams of x-rays in very short bursts that can be more than ten billion times brighter than pulses from other x-ray sources. These lasers find applications in sciences ranging from astrophysics to structural biology, and could allow us to obtain images of single macromolecules when these are injected into the x-ray beam. A macromolecule injected into vacuum in a microdroplet will be affected by evaporation and by the dynamics of the carrier liquid before being hit by the x-ray pulse. Simulations of neutral and charged water droplets were performed to predict structural changes and changes of temperature due to evaporation. The results are discussed in the aspect of single molecule imaging. Further studies show ionization caused by the intense x-ray radiation. These simulations reveal the development of secondary electron cascades in water. Other studies show the development of these cascades in KI and CsI where experimental data exist. The results are in agreement with observation, and show the temporal, spatial and energetic evolution of secondary electron cascades in the sample. X-ray diffraction is sensitive to structural changes on the length scale of chemical bonds. Using a short infrared pump pulse to trigger structural changes, and a short x-ray pulse for probing it, these changes can be studied with a temporal resolution similar to the pulse lengths. Time resolved diffraction experiments were performed on a phase transition during resolidification of a non-thermally molten InSb crystal. The experiment reveals the dynamics of crystal regrowth. Computer simulations were performed on the infrared laser-induced melting of bulk ice, giving a comprehension of the dynamics and the wavelength dependence of melting. These studies form a basis for planning experiments with x-ray lasers.