In this thesis, Molecular Dynamics simulations of shocked single crystals of Copper and Iron are studied using simulated X-ray diffraction. Strains and volumetric compression in modeled Copper crystals shock-compressed on picosecond time-scales are found. By comparing the shifts in the second and fourth diffraction orders, the density of dislocations is calculated. In Iron, simulated X-ray diffraction is used to verify the modelling of the α-ε phase transition induced by shock-compression on picosecond time-scales. No plastic deformation of Iron is found in the studied pressure range of ~ 15-53 GPa. The results are then compared with data from in situ X-ray diffraction experiments of laser-shocked single crystals. Near-hydrostatic compression of shock-compressed Copper on nanosecond time-scales is confirmed using a new wide-angle film diagnostic capturing diffraction from multiple crystal planes. Also, the first in situ X-ray diffraction evidence of the onset of the α-ε phase transition in laser-shocked single crystal Iron is shown. No plastic yield of the crystal lattice is found, which is in agreement with the simulation results. Results from both the Molecular Dynamics simulations and experiments are used to suggest enhancements in computer modelling of shocked crystals, as well as future experimental studies. In particular, the need for a measurement of dislocation densities during the shock wave passage through a crystal is highlighted, and a method enabling such a measurement is proposed.