Organic carbon (OC) and elemental carbon (EC) together constitute a substantial proportion of airborne particulate matter (PM). Insight into the sources of this major contributor to PM is important for policies to mitigate the impact of PM on human health and climate change. In recent years measurement of the abundance of the radioisotope of carbon ((14)C) in samples of PM by accelerator mass spectrometry has been used to help quantify the relative contributions from sources of fossil carbon and contemporary carbon. This review provides an introduction to the different sources of carbon within PM and the role of (14)C measurements, a description of the preparation of PM samples and of the instrumentation used to quantify (14)C, and a summary of the results and source apportionment methods reported in published studies since 2004. All studies report a sizable fraction of the carbonaceous PM as of non-fossil origin. Even for PM collected in urban locations, the proportions of non-fossil carbon generally exceed 30 %; typically the proportion in urban background locations is around 40-60 % depending on the local influence of biomass burning. Where values have been measured directly, proportions of non-fossil carbon in EC are lower than in OC, reflecting the greater contribution of fossil-fuel combustion to EC and the generally small sources of contemporary EC. Detailed source apportionment studies point to important contributions from biogenic-derived secondary OC, consistent with other evidence of a ubiquitous presence of heavily oxidized background secondary OC. The review concludes with some comments on current issues and future prospects, including progress towards compound-class and individual-compound-specific (14)C analyses.