Many different kinds of paleoclimatic, geological and archaeological records can be characterized by measuring their radionuclide concentrations using accelerator mass spectrometry (AMS). The purpose of this paper is to highlight some applications of AMS, using studies conducted at the Arizona AMS Facility as examples. These include studies of 14C, 10Be, 26Al, and 129I. The work can be generally divided into two types: (1) methodological studies designed to refine and improve the capabilities of AMS, and (2) studies which utilize radiogenic isotopes as geochronometers or as geochemical tracers. Studies of the first type include the development of our 26Al measurement capabilities, the construction on an automated sample preparation line and the construction of a plasma oxidation line. Studies of the latter type include 14C dating of corals, speleothems and bones; new records of 10Be from marine sediments and extraterrestrial materials; and 129I studies of the pathways of this isotope in the surface ocean.