The history and advances of neutronics calculations at Los Alamos during the Manhattan Project through the present is reviewed. We briefly summarize early simpler, and more approximate neutronics methods. We then motivate the need to better predict neutronics behavior through consideration of theoretical equations, models and algorithms, experimental measurements, and available computing capabilities and their limitations. These, coupled with increasing post-war defense needs, and the invention of electronic computing led to the creation of Monte Carlo neutronics transport. As a part of the history, we note the crucial role that the scientific comradery between the great Los Alamos scientists played in the process. We focus heavily on these early developments and the subsequent successes of Monte Carlo and its applications to problems of national defense at Los Alamos. We cover the early methods, algorithms, and computers, electronic and women pioneers, that enabled Monte Carlo to spread to all areas of science.