Models of molecular sequence evolution have been a pivotal source of insight into the biological mechanisms and forces of evolution. Model development and improvements in computational capacity have allowed for increasingly sophisticated analyses in the last four decades, however, many studies still use twenty year old GTR+[Gamma] models for convenience and computational tractability. Here we present a new model in the branch-site random effects likelihood framework, Adaptive Branch-Site Random Effects Likelihood (aBSREL), that is more sensitive and an order of magnitude faster than previous branch-site models. We demonstrate the effectiveness of aBSREL at detecting episodic diversifying selection using simulated sequences and previously studied empirical alignments. As part of an ongoing investigation into the importance of modeling natural selection and especially selection heterogeneity in molecular dating analyses, we undertake a detailed study of ten potentially ancient viral lineages using aBSREL, comparing our estimates with previously published molecular dating, historical, and fossil estimates. We also present two special purpose models within the branch- site REL framework and the addition of massively parallel accelerators such as Graphics Processing Units to the high performance computing resources addressable by HyPhy. The first of these two models, RELAX, is purpose built to detect relaxed selection while the BUSTED model uses a priori partitioning and sublinear complexity scaling to further improve computational tractability. Both models are demonstrated on simulated and empirical datasets and compared to current state of the art alternatives from the literature. These models represent a substantial expansion to the branch-site REL framework and are available for use in the HyPhy software package and on the Datamonkey.org webserver