Brief biographical sketch of the author -- Historical development of accelerator mass spectrometry--1977 -- Historical development of accelerator mass spectrometry--1978-80 -- The development of tandem electrostatic accelerators -- Instrumentation for accelerator mass spectrometry -- The legacy of the atomic bombing of Hiroshima and Nagasaki -- The initial peopling of the Americas -- The American Indians, the Vikings and Columbus -- Nuclear power, nuclear weapons and nuclear waste -- Carbon dating the Turin Shroud -- The iceman, the Dead Sea Scrools and more -- Some thoughts of future developments of AMS.