Accelerator mass spectrometry (AMS) is sometimes called 'the art of counting atoms one by one'. In addition to counting individual atoms, AMS is also capable to determine both mass number (A) and atomic number (Z). Since an atom (also called a nuclide) is unambiguously characterized by the proton number (Z) and the neutron number (N = A − Z), a rare nuclide can be well separated from possible background events, and extremely low abundances of specific nuclides can be measured. In general, the use of an accelerator system as a mass spectrometer improves the isotope abundance sensitivity by many orders of magnitude as compared to standard mass spectrometry (without an accelerator). In particular, AMS provides the means to measure minute traces of long-lived radioisotopes of cosmogenic and/or anthropogenic origin in essentially every domain of our environment at large. This allows one to use AMS for performing research in many different areas, ranging from archaeology to astrophysics. In this review, an update of the current status of AMS and an outlook to future developments in both technical and applied aspects will be presented. The transition from Mass Spectrometry (MS) to Accelera tor Mass Spectrometry (AMS)