The ability to accurately model protein structures at the atomistic level underpins efforts to understand protein folding, to engineer natural proteins predictably and to design proteins de novo. Homology-based methods are well established and produce impressive results. However, these are limited to structures presented by and resolved for natural proteins. Addressing this problem more widely and deriving truly ab initio models requires mathematical descriptions for protein folds, the means to decorate these with natural, engineered or de novo sequences, and methods to score the resulting models.