Paul Urysohn and Karl Menger were the prime developers of dimension theory in the early 1920s. As young mathematicians from different countries, they initially developed their differing, though remarkably similar, theories independently, each not knowing of the other’s work. Each put together an extensive set of results. Then as various mathematicians sorted out the differences, the two theories became joined together, resulting in a reasonably unified theory derived from the efforts of several important mathematicians. Not surprisingly, the history exhibits ups and downs.