Between 1942 and 2010 there were >134 proposed molecular level representations ( models) of coal. While they spanned the rank range, bituminous representations are the bulk, with far fewer lignite, and very few subbituminous or anthracite representations. They have transitioned from predominantly 2D pen and paper drawings into 3D computational structures, and have recently increased in complexity, and to a limited degree, in scale. Advances in analytical techniques as well as modeling software, and computation power have resulted in improved partial representations of coal structure. Computer aided design has helped to overcome some of the challenges in model construction for a few models. Yet generally it is the capturing of the constitution of coal that remains elusive. Evaluation of physical parameters and behavior observations has aided our confidence in the representations but models are typically generated for a specific use. No model has faced the gambit of "tests''. (C) 2011 Elsevier Ltd. All rights reserved.