Wide energy gap semiconductors are broadly recognized as promising materials for novel electronic and opto-electronic device applications. As informed device design requires a firm grasp on the material properties of the underlying electronic materials, the electron transport that occurs within the wide energy gap semiconductors has been the focus of considerable study over the years. We review analyses of the electron transport within some wide energy gap semiconductors of current interest. In this thesis, I primarily focus on the electron transport that occurs within the wurtzite and zinc-blende phases of gallium nitride and indium nitride, these materials being of great current interest to the wide energy gap semiconductor community; indium nitride, while not a wide energy gap semiconductor of itself, is included as it is often alloyed with other wide energy gap semiconductors. The electron transport that occurs within zinc-blende gallium arsenide has also been considered. Most of the discussion focus on the steady-state and transient electron transport results obtained from the ensemble semi-classical three-valley Monte Carlo simulations of the electron transport within these materials.The evolution of the field, a survey of the current literature, and some applications for the results will also be featured. Based on this analysis, we have drawn the following conclusions. First, it is found that all of the velocityfield characteristics corresponding to the materials under investigation in this analysis exhibit peaks, regions of negative differential mobility, and regions of high-field saturation. Wurtzite Indium nitride, with its small electron effective mass, exhibits the highest peak electron drift velocity. The transient overshoot observed for the case of wurtzite Indium nitride is also found to be the most pronounced of all of the materials considered in this analysis. This suggests that the wurtzite phase of Indium nitride and its zinc-blende counterpart may offer great potential for future electron device applications. vi Rensselaer Polytechnic Institute, for example, was one of the first researchers to explore the wide energy gap semiconductors, GaN and InN, through the use of Monte Carlo electron transport simulations. In fact, some of his initial explorations into the nature of the electron transport within these materials were performed by him in concert with Dr. O'Leary. Dr. Shur and Dr. O'Leary have established a vigorous and active research collaboration, and the papers that I wrote within the scope of my doctoral studies were merely the latest of a large number of publications that have arisen from this collaboration. Dr. Shur commented on each manuscript, and made some suggestions in terms of interpreting the results. These definitely helped improve the clarity and effectiveness of my publications.