Organic species are an important but poorly characterized constituent of airborne particulate matter. A quantitative understanding of the organic fraction of particles (organic aerosol, OA) is necessary to reduce some of the largest uncertainties that confound the assessment of the radiative forcing of climate and air quality management policies. In recent years, aerosol mass spectrometry has been increasingly relied upon for highly time-resolved characterization of OA chemistry and for elucidation of aerosol sources and lifecycle processes. Aerodyne aerosol mass spectrometers (AMS) are particularly widely used, because of their ability to quantitatively characterize the size-resolved composition of submicron particles (PM(1)). AMS report the bulk composition and temporal variations of OA in the form of ensemble mass spectra (MS) acquired over short time intervals. Because each MS represents the linear superposition of the spectra of individual components weighed by their concentrations, multivariate factor analysis of the MS matrix has proved effective at retrieving OA factors that offer a quantitative and simplified description of the thousands of individual organic species. The sum of the factors accounts for nearly 100% of the OA mass and each individual factor typically corresponds to a large group of OA constituents with similar chemical composition and temporal behavior that are characteristic of different sources and/or atmospheric processes. The application of this technique in aerosol mass spectrometry has grown rapidly in the last six years. Here we review multivariate factor analysis techniques applied to AMS and other aerosol mass spectrometers, and summarize key findings from field observations. Results that provide valuable information about aerosol sources and, in particular, secondary OA evolution on regional and global scales are highlighted. Advanced methods, for example a-priori constraints on factor mass spectra and the application of factor analysis to combined aerosol and gas phase data are discussed. Integrated analysis of worldwide OA factors is used to present a holistic regional and global description of OA. Finally, different ways in which OA factors can constrain global and regional models are discussed.