Methane is a powerful greenhouse gas and is targeted for emissions mitigation by the US state of California and other jurisdictions worldwide1,2. Unique opportunities for mitigation are presented by point-source emitters-surface features or infrastructure components that are typically less than 10 metres in diameter and emit plumes of highly concentrated methane3. However, data on point-source emissions are sparse and typically lack sufficient spatial and temporal resolution to guide their mitigation and to accurately assess their magnitude4. Here we survey more than 272,000 infrastructure elements in California using an airborne imaging spectrometer that can rapidly map methane plumes5-7. We conduct five campaigns over several months from 2016 to 2018, spanning the oil and gas, manure-management and waste-management sectors, resulting in the detection, geolocation and quantification of emissions from 564 strong methane point sources. Our remote sensing approach enables the rapid and repeated assessment of large areas at high spatial resolution for a poorly characterized population of methane emitters that often appear intermittently and stochastically. We estimate net methane point-source emissions in California to be 0.618 teragrams per year (95 per cent confidence interval 0.523-0.725), equivalent to 34-46 per cent of the state's methane inventory8 for 2016. Methane 'super-emitter' activity occurs in every sector surveyed, with 10 per cent of point sources contributing roughly 60 per cent of point-source emissions-consistent with a study of the US Four Corners region that had a different sectoral mix9. The largest methane emitters in California are a subset of landfills, which exhibit persistent anomalous activity. Methane point-source emissions in California are dominated by landfills (41 per cent), followed by dairies (26 per cent) and the oil and gas sector (26 per cent). Our data have enabled the identification of the 0.2 per cent of California's infrastructure that is responsible for these emissions. Sharing these data with collaborating infrastructure operators has led to the mitigation of anomalous methane-emission activity10.