The idea that the world might ultimately be made up of indivisible lumps of matter ("atoms") is thousands of years old. However, it is only in the past three centuries that we have really started to gather credible evidence of it. By 1912 it had become clear that while atoms do exist, they are certainly not indivisible. In the subsequent century's work, probing the sub-atomic structure of the universe, we have made some very surprising discoveries, the practical applications of which are yet to be fully exploited. This lecture will review the development of the atomic theory, beginning with the Greeks and early periodic tables, and ending with the latest developments in the exploitation of quantum mechanics.