Since its first observation, a decade ago, high harmonic generation (HHG) in crystals has proved to be an efficient, controllable and compact source of coherent XUV radiation. In this thesis, we investigate HHG in 2D materials, particularly graphene, and in different semiconductor crystals mainly zinc oxide, silicon, gallium arsenide and magnesium oxide. We find that the laser properties, such as its intensity, polarization and ellipticity, and the crystal properties are interrelated. Moreover, we shed the light on the role of the linear and nonlinear propagation effects mainly the Kerr effect, upon laser interaction with the crystal, which can significantly influence the high harmonic generation efficiency. Although this presents major lim...