Provenance analysis of sediments is aimed at reconstructing the parent-rock assemblages of sediments and the climatic-physiographic conditions under which sediments formed. Inferring sediment provenance from the final product, a basin fill, is anything but straightforward because the detrital spectrum evolves as the sediment is transported along the pathway from source to basin. Successful provenance analysis requires that the nature and extent of compositional and textural modifications to the detrital spectrum be recognised, if not quantified. The history of quantification in sediment-provenance studies is summarised and illustrated by tracking two fundamental ideas: the concept of the sediment-petrological province or petrofacies, and the relation between sandstone composition and (plate) tectonic environment. Progress in sedimentary provenance analysis has been closely linked with advancements in measurement technology. A brief survey of modern data-acquisition tools illustrates the possibilities and limitations of modern provenance research. An operational definition of Quantitative Provenance Analysis (QPA) is presented in which the central role of mass balance is acknowledged. Extension of this definition to include quantitative predictions obtained by forward modelling (computer simulation) of sediment production, as well as methodological improvements in data acquisition and processing is needed to cover likely future developments in QPA. The contributions to the special issue "Quantitative Provenance Analysis of Sediments" illustrate the intrinsic multidisciplinarity and rapid expansion of QPA.