High harmonic generation (HHG) in solids has two main applications. First, HHG is an all-solid-state source of coherent attosecond very ultraviolet (VUV) radiation. As such, it presents a promising source for attosecond science. The ultimate goal of attosecond science is to make spatially and temporally resolved movies of microscopic processes, such as the making and breaking of molecular bonds. Second, the HHG process itself can be used to spatially and temporally resolve fast processes in the condensed matter phase, such as charge shielding, multi-electron interactions, and the dynamics and decay of collective excitations. The main obstacles to realize these goals are: the very low efficiency of HHG in solids and incomplete understanding of the ultrafast dynamics of the complex many-body processes occurring in the condensed matter phase. The theoretical analysis developed in this thesis promises progress along both directions. First, it is demonstrated that nanoengineering by using lower-dimensional solids can drastically enhance the efficiency of HHG. The effect of quantum confinement on HHG in semiconductor materials is studied by systematically varying the confinement width along one and two directions transverse to the laser polarization. Our analysis shows growth in high harmonic efficiency concurrent with a reduction of ionization. This decrease in ionization comes as a consequence of an increased band gap resulting from the confinement. The increase in harmonic efficiency results from a restriction of wave packet spreading, leading to greater re-collision probability. Consequently, nanoengineering of one and two-dimensional nanosystems may prove to be a viable means to increase harmonic yield and photon energy in semiconductor materials driven by intense laser fields. Thus, it will contribute towards the development of reliable, all-solid-state, small-scale, and laboratory attosecond pulse sources. Second, it is shown that HHG from impurities can be used to tomographically reconstruct impurity orbitals. A quasi-classical three-step model is developed that builds a basis for impurity tomography. HHG from impurities is found to be similar to the high harmonic generation in atomic and molecular gases with the main difference coming from the non-parabolic nature of the bands. This opens a new avenue for strong field atomic and molecular physics in the condensed matter phase and allows many of the processes developed for gas-phase attosecond science to be applied to the condensed matter phase. As a first application, my conceptual study demonstrates the feasibility of tomographic measurement of impurity orbitals. Ultimately, this could result in temporally and spatially resolved measurements of electronic processes in impurities with potential relevance to quantum information sciences, where impurities are prime candidates for realizing qubits and single photon sources. Although scanning tunneling microscope (STMs) can measure electron charge distributions in impurities, measurements are limited to the first few surface layers and ultrafast time resolution is not possible yet. As a result, HHG tomography can add complementary capacities to the study of impurities.