For modern semiconductor heterostructures containing multiple populations of distinct carrier species, conventional Hall and resistivity data acquired at a single magnetic field provide far less information than measurements as a function of magnetic field. However, the extraction of reliable and accurate carrier densities and mobilities from the field-dependent data can present a number of difficult challenges, which were never fully overcome by earlier methods such as the multi-carrier fit, the mobility spectrum analysis of Beck and Anderson, and the hybrid mixed-conduction analysis. More recently, in order to overcome the limitations of those methods, several research groups have contributed to development of the quantitative mobility spectrum analysis (QMSA), which is now available as a commercial product. The algorithm is analogous to a fast Fourier transform, in that it transforms from the magnetic field B domain to the mobility ž domain. QMSA converts the field-dependent Hall and resistivity data into a visually-meaningful transformed output, comprising the conductivity density of electrons and holes in the mobility domain. In this article, we apply QMSA to both synthetic and real experimental data that are representative of modern semiconductor structures.