The deployment of many-body quantum chemistry methods onto massively parallel high-performance computing (HPC) platforms is reviewed. The particular focus is on highly accurate methods that have become popular in predictive description of chemical phenomena, such as the coupled-cluster method. The account of relevant literature is preceded by a discussion of the modern and near-future HPC landscape and the relevant computational traits of the many-body methods, in their canonical and reduced-scaling formulations, that underlie the challenges in their HPC realization.