We deployed a high-resolution proton-transfer-reaction time-of-flight mass spectrometer (PTR-TOF-MS) to measure biomass-burning emissions from peat, crop residue, cooking fires, and many other fire types during the fourth Fire Lab at Missoula Experiment (FLAME-4) laboratory campaign. A combination of gas standard calibrations and composition sensitive, mass-dependent calibration curves was applied to quantify gas-phase non-methane organic compounds (NMOCs) observed in the complex mixture of fire emissions. We used several approaches to assign the best identities to most major "exact masses", including many high molecular mass species. Using these methods, approximately 80-96% of the total NMOC mass detected by the PTR-TOF-MS and Fourier transform infrared (FTIR) spectroscopy was positively or tentatively identified for major fuel types. We report data for many rarely measured or previously unmeasured emissions in several compound classes including aromatic hydrocarbons, phenolic compounds, and furans; many of these are suspected secondary organic aerosol precursors. A large set of new emission factors (EFs) for a range of globally significant biomass fuels is presented. Measurements show that oxygenated NMOCs accounted for the largest fraction of emissions of all compound classes. In a brief study of various traditional and advanced cooking methods, the EFs for these emissions groups were greatest for open three-stone cooking in comparison to their more advanced counterparts. Several little-studied nitrogen-containing organic compounds were detected from many fuel types, that together accounted for 0.1-8.7% of the fuel nitrogen, and some may play a role in new particle formation.