Abstract We update the capabilities of the open-knowledge software instrument Modules for Experiments in Stellar Astrophysics (MESA). RSP is a new functionality in MESAstar that models the nonlinear radial stellar pulsations that characterize RR Lyrae, Cepheids, and other classes of variable stars. We significantly enhance numerical energy conservation capabilities, including during mass changes. For example, this enables calculations through the He flash that conserve energy to better than 0.001%. To improve the modeling of rotating stars in MESA, we introduce a new approach to modifying the pressure and temperature equations of stellar structure, as well as a formulation of the projection effects of gravity darkening. A new scheme for tracking convective boundaries yields reliable values of the convective core mass and allows the natural emergence of adiabatic semiconvection regions during both core hydrogen- and helium-burning phases. We quantify the parallel performance of MESA on current-generation multicore architectures and demonstrate improvements in the computational efficiency of radiative levitation. We report updates to the equation of state and nuclear reaction physics modules. We briefly discuss the current treatment of fallback in core-collapse supernova models and the thermodynamic evolution of supernova explosions. We close by discussing the new MESA Testhub software infrastructure to enhance source code development.