We report the state of the field of High-Power Fixed-Field Accelerators (with an emphasis on cyclotrons) as discussed by international experts during a three-day workshop of the same name in 2021. The workshop was part of the Snowmass'21 Community Planning Exercise. Here, we take stock of the world inventory of high-power fixed-field accelerators, assess available beam currents and beam powers, and investigate limitations. Furthermore, we evaluate the role of these machines in particle physics, directly used or as injectors to other machines, and in industry, as drivers for (medical) isotope production and, potentially, for accelerator-driven systems and sub-critical reactors. Finally, we discuss novel concepts and cutting-edge developments to push the available current higher at several energy scales, thereby increasing relative power. Highlights include new spiral inflector types, direct RFQ injection, H₂⁺ acceleration, utilizing vortex motion, and self-extraction schemes. We also discuss modern computational frameworks to optimize accelerators more efficiently, and better describe the relevant physical processes in simulations.