While a quantitative climate theory of tropical cyclone formation remains elusive, considerable progress has been made recently in our ability to simulate tropical cyclone climatologies and to understand the relationship between climate and tropical cyclone formation. Climate models are now able to simulate a realistic rate of global tropical cyclone formation, although simulation of the Atlantic tropical cyclone climatology remains challenging unless horizontal resolutions finer than 50 km are employed. This article summarizes published research from the idealized experiments of the Hurricane Working Group of U.S. Climate and Ocean: Variability, Predictability and Change (CLIVAR). This work, combined with results from other model simulations, has strengthened relationships between tropical cyclone formation rates and climate variables such as midtropospheric vertical velocity, with decreased climatological vertical velocities leading to decreased tropical cyclone formation. Systematic differences are shown between experiments in which only sea surface temperature is increased compared with experiments where only atmospheric carbon dioxide is increased. Experiments where only carbon dioxide is increased are more likely to demonstrate a decrease in tropical cyclone numbers, similar to the decreases simulated by many climate models for a future, warmer climate. Experiments where the two effects are combined also show decreases in numbers, but these tend to be less for models that demonstrate a strong tropical cyclone response to increased sea surface temperatures. Further experiments are proposed that may improve our understanding of the relationship between climate and tropical cyclone formation, including experiments with two-way interaction between the ocean and the atmosphere and variations in atmospheric aerosols.