Fire is an important influence on the global patterns of vegetation structure and composition. Wildfire is included as a distinct process in many dynamic global vegetation models but limited current understanding of fire regimes restricts these models' ability to reproduce more than the broadest geographic patterns. Here we present a statistical analysis of the global controls of remotely sensed burnt area (BA), fire size (FS), and a derived metric related to fire intensity (FI). Separate generalized linear models were fitted to observed monthly fractional BA from the Global Fire Emissions Database (GFEDv4), median FS from the Global Fire Atlas, and median fire radiative power from the MCD14ML dataset normalized by the square root of median FS. The three models were initially constructed from a common set of 16 predictors; only the strongest predictors for each model were retained in the final models. It is shown that BA is primarily driven by fuel availability and dryness; FS by conditions promoting fire spread; and FI by fractional tree cover and road density. Both BA and FS are constrained by landscape fragmentation, whereas FI is constrained by fuel moisture. Ignition sources (lightning and human population) were positively related to BA (after accounting for road density), but negatively to FI. These findings imply that the different controls on BA, FS and FI need to be considered in process-based models. They highlight the need to include measures of landscape fragmentation as well as fuel load and dryness, and to pay close attention to the controls of fire spread.