The ATLAS experiment at the Large Hadron Collider has a broad physics programme ranging from precision measurements to direct searches for new particles and new interactions, requiring ever larger and ever more accurate datasets of simulated Monte Carlo events. Detector simulation with GEANT4 is accurate but requires significant CPU resources. Over the past decade, ATLAS has developed and utilized tools that replace the most CPU-intensive component of the simulation -- the calorimeter shower simulation -- with faster simulation methods. Here, AtlFast3, the next generation of high-accuracy fast simulation in ATLAS is introduced. AtlFast3 combines parameterized approaches with machine-learning techniques and is deployed to meet current and future computing challenges and simulation needs of the ATLAS experiment. With highly accurate performance and a new ability to model substructure within jets, AtlFast3 is designed to be used to simulate large numbers of events for a wide range of physics processes.