The versatility and sensitivity of the quadrupole ion trap tandem mass spectrometer has been applied to the determination of polychlorodibenzo-p-dioxins (PCDDs) and polychlorodibenzofurans (PCDFs), and of polychlorinated biphenyls (PCBs). A brief introduction to the theory of ion confinement in a quadrupole ion trap permits discussion of ion trajectory stability, mass-selective ion ejection, the frequencies of ion motion, and the role of resonant excitation of ion motion. The tandem mass spectrometric examination of PCDDs and PCDFs eluting and co-eluting from a gas chromatographic column is described. Illustrative examples are given of the analysis of field samples containing PCDDs and PCDFs. A comparison is presented of the performance of each of a quadrupole ion trap tandem mass spectrometer, a triple stage quadrupole mass spectrometer, and a sector instrument of relatively high mass resolution for the determination of PCDDs and PCDFs. This comparison is made with respect to instrument tuning, calibration plots, detection limits, ion signals at low concentration, relative response factors, ionization cross-sections, and the examination of field samples. The application of quadrupole ion trap tandem mass spectrometry to the examination of PCBs is focused upon those PCB congeners that have the greatest toxicity. 39 congeners of the total of 209 PCB congeners have been identified as having the greatest toxicities. Chemical ionization has been used for the determination of co-eluting congeners #77 and #110 where the toxicity of the former is much greater than that of the latter. An analytical protocol, based on the variation of molecular ion fragmentation according to the degree (or absence) of chlorine ortho-substitution, has been proposed for distinguishing between toxic and nontoxic PCB congeners.