This paper reviews the physics of extremely high current propagation in dense materials. We consider explicitly the problem of the generation of high-current, high-particle energy propagation arising from laser ionization in otherwise neutral targets. The paper concentrates upon the recent experimental results of measurements of the distribution of the laser-generated fast electrons, both in space as well as in energy. The emphasis is primarily to put into physical context the growing number of experimental observations under widely varying conditions. Little or no effort is made to summarize the theoretical or modeling work because of manuscript size limitations; however, when possible, experimental observations are tied to relevant attempts to model the observed behavior. The fundamental conclusion is that fast electron propagation, at a current density and kinetic energy relevant to fast ignition, is far from a solved problem and that target design for fast ignition will have to play a significant role to overcome some of the emerging physical obstacles.