Wide energy gap semiconductors are broadly recognized as promising materials for novel electronic and optoelectronic device applications. As informed device design requires a firm grasp of 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. In an effort to provide some perspective on this rapidly evolving and burgeoning field of research, we review analyzes of the electron transport within some wide energy gap semiconductors of current interest in this paper. In order to narrow the scope of this review, we will primarily focus on the electron transport that occurs within the wurtzite phases of gallium nitride, aluminum nitride, indium nitride, and zinc oxide in this review, these materials being of great current interest to the wide energy gap semiconductor community; indium nitride, while not a wide energy gap semiconductor in of itself, is included as it is often alloyed with other wide energy gap semiconductors, the resultant alloys being wide energy gap semiconductors themselves. The electron transport that occurs within zinc-blende gallium arsenide is also considered, albeit primarily for bench-marking purposes. Most of our discussion will focus on results obtained from our ensemble semi-classical three-valley Monte Carlo simulations of the electron transport within these materials, our results conforming with state-of-the-art wide energy gap semiconductor orthodoxy. A brief tutorial on the Monte Carlo electron transport simulation approach, this approach being used to generate the results presented herein, is also provided. Steady-state and transient electron transport results are presented. The evolution of the field, and a survey of the current literature, are also featured. We conclude our review by presenting some recent developments on the electron transport within these materials.