Accelerator mass spectroscopy (AMS) can be used for efficient detection of long-lived isotopes at part-per-quadrillion sensitivities with good precision. In this article we present an overview of AMS and its recent use in archaeology, geochemistry and biomolecular tracing. All AMS systems use cesium sputter ion sources to produce negative ions from a small button of a solid sample containing the element of interest, such as graphite, metal halide, or metal oxide, often mixed with a metal powder as binder and thermal conductor. Experience shows that both natural and biomedical samples are compatible in a single AMS system, but few other AMS sites make routine {sup 14}C measurements for both dating and tracing. AMS is, in one sense, just `a very sensitive decay counter`, but if AMS sensitivity is creatively coupled to analytical chemistry of certain isotopes, whole new areas of geosciences, archaeology, and life sciences can be explored. 29 refs., 2 figs., 1 tab.