Isoprene is the dominant non-methane organic compound emitted to the atmosphere1-3. It drives ozone and aerosol production, modulates atmospheric oxidation and interacts with the global nitrogen cycle4-8. Isoprene emissions are highly uncertain1,9, as is the nonlinear chemistry coupling isoprene and the hydroxyl radical, OH-its primary sink10-13. Here we present global isoprene measurements taken from space using the Cross-track Infrared Sounder. Together with observations of formaldehyde, an isoprene oxidation product, these measurements provide constraints on isoprene emissions and atmospheric oxidation. We find that the isoprene-formaldehyde relationships measured from space are broadly consistent with the current understanding of isoprene-OH chemistry, with no indication of missing OH recycling at low nitrogen oxide concentrations. We analyse these datasets over four global isoprene hotspots in relation to model predictions, and present a quantification of isoprene emissions based directly on satellite measurements of isoprene itself. A major discrepancy emerges over Amazonia, where current underestimates of natural nitrogen oxide emissions bias modelled OH and hence isoprene. Over southern Africa, we find that a prominent isoprene hotspot is missing from bottom-up predictions. A multi-year analysis sheds light on interannual isoprene variability, and suggests the influence of the El Niño/Southern Oscillation.