Hammer, whose father founded the American Communist Party, began a successful career in importing and exporting pharmaceuticals to the newly-formed Soviet Union, where he lived during the 1920s. After returning to the US, he invested in Occidental Petroleum, and continued personal and business dealings with the Soviet Union, despite Cold War taboos on such dealings by Americans. In later years he lobbied for peace between America and the Communist countries of the world.
The discrepancy between Hammer's open sympathy for the Soviet Union and his success as a capitalist, as well as his involvement in international affairs and politics, have made Hammer a subject of suspicion and conspiracy theory for the American right.
Hammer was also an avid collector of Impressionist and Post-Impressionist paintings. His personal donation forms the core of the permanent collection of the UCLA Hammer Museum in Los Angeles, California.
Despite popular myth, the relation between Hammer's name and the household product Arm and Hammer baking soda is coincidental. The pun was not lost on Hammer, though: during the 1980s, he attempted to buy Church and Dwight, makers of Arm and Hammer, and eventually sat on its board of directors.