Hector is an open-source reduced-form complexity climate-carbon cycle model. It is a computationally efficient source of climate information, capable of completing a century-long run in a fraction of a second. Hector models critical Earth system processes on a global and annual basis. Here we present results from the latest version of the model, Hector V3.2.0, which includes new model features and implements recent advancements in science (e.g., radiative forcing calculations, carbon cycle, etc.). Hector's historical results are consistent with CO2 concentrations and global mean surface temperature observations while also producing future temperature projections that are consistent with more complex Earth System Model output data from the Sixth Coupled Model Intercomparison Project. Hector is a flexible, performant, and robust simulator of contemporary and 21st-century global climate with a wide range of possible applications to several areas of scientific research and educational outreach.