As one in a series of articles on Canadian contributions to mass spectrometry, this review begins with an outline of the history of accelerator mass spectrometry (AMS), noting roles played by researchers at three Canadian AMS laboratories. After a description of the unique features of AMS, three examples, (14)C, (10)Be, and (129)I are given to illustrate the methods. The capabilities of mass spectrometry have been extended by the addition of atomic isobar selection, molecular isobar attenuation, further ion acceleration, followed by ion detection and ion identification at essentially zero dark current or ion flux. This has been accomplished by exploiting the techniques and accelerators of atomic and nuclear physics. In 1939, the first principles of AMS were established using a cyclotron. In 1977 the selection of isobars in the ion source was established when it was shown that the (14)N(-) ion was very unstable, or extremely difficult to create, making a tandem electrostatic accelerator highly suitable for assisting the mass spectrometric measurement of the rare long-lived radioactive isotope (14)C in the environment. This observation, together with the large attenuation of the molecular isobars (13)CH(-) and (12)CH 2(-) during tandem acceleration and the observed very low background contamination from the ion source, was found to facilitate the mass spectrometry of (14)C to at least a level of (14)C/C ~ 6 × 10(-16), the equivalent of a radiocarbon age of 60,000 years. Tandem Accelerator Mass Spectrometry, or AMS, has now made possible the accurate radiocarbon dating of milligram-sized carbon samples by ion counting as well as dating and tracing with many other long-lived radioactive isotopes such as (10)Be, (26)Al, (36)Cl, and (129)I. The difficulty of obtaining large anion currents with low electron affinities and the difficulties of isobar separation, especially for the heavier mass ions, has prompted the use of molecular anions and the search for alternative methods of isobar separation. These techniques are discussed in the latter part of the review.