The work contained in this dissertation is focused on the optical properties of direct band gap semiconductors which crystallize in a wurtzite structure: more specifically, the III-nitrides and ZnO. By using cathodoluminescence spectroscopy, many of their properties have been investigated, including band gaps, defect energy levels, carrier lifetimes, strain states, exciton binding energies, and effects of electron irradiation on luminescence. Part of this work is focused on p-type Mg-doped GaN and InGaN. These materials are extremely important for the fabrication of visible light emitting diodes and diode lasers and their complex nature is currently not entirely understood. The luminescence of Mg-doped GaN films has been correlated with electrical and structural measurements in order to understand the behavior of hydrogen in the material. Deeply-bound excitons emitting near 3.37 and 3.42 eV are observed in films with a significant hydrogen concentration during cathodoluminescence at liquid helium temperatures. These radiative transitions are unstable during electron irradiation. Our observations suggest a hydrogen-related nature, as opposed to a previous assignment of stacking fault luminescence. The intensity of the 3.37 eV transition can be correlated with the electrical activation of the Mg acceptors. Next, the acceptor energy level of Mg in InGaN is shown to decrease significantly with an increase in the indium composition. This also corresponds to a decrease in the resistivity of these films. In addition, the hole concentration in multiple quantum well light emitting diode structures is much more uniform in the active region when Mg-doped InGaN (instead of Mg-doped GaN) is used. These results will help improve the efficiency of light emitting diodes, especially in the green/yellow color range. Also, the improved hole transport may prove to be important for the development of photovoltaic devices. Cathodoluminescence studies have also been performed on nanoindented ZnO crystals. Bulk, single crystal ZnO was indented using a sub-micron spherical diamond tip on various surface orientations. The resistance to deformation (the "hardness") of each surface orientation was measured, with the c-plane being the most resistive. This is due to the orientation of the easy glide planes, the c-planes, being positioned perpendicularly to the applied load. The a-plane oriented crystal is the least resistive to deformation. Cathodoluminescence imaging allows for the correlation of the luminescence with the regions located near the indentation. Sub-nanometer shifts in the band edge emission have been assigned to residual strain the crystals. The a- and m-plane oriented crystals show two-fold symmetry with regions of compressive and tensile strain located parallel and perpendicular to the ±c-directions, respectively. The c-plane oriented crystal shows six-fold symmetry with regions of tensile strain extending along the six equivalent a-directions.