The Monte Carlo method, largely the brainchild of Stanislaw Ulam and first implemented by John von Neumann, depends upon the use of digital computers and is therefore very much a product of post-WW2 technological developments; even though one could argue that the Buffon’s Needle estimate was an ancestor of the technique. The probabilistic nature of the method makes it a good choice for modeling those physical phenomena which involve similarly random motions at the atomic scale; a particularly good example being that of mass diffusion. The present volume comprises a compilation of selected Monte Carlo studies of diffusion in borides, carbides, diamond, graphene, graphite, hydrides, ice, metals, oxides, semiconductors, sulfides, zeolites and other materials. General aspects of diffusion are also covered. The 516 entries cover the period from 1966 to 2014.