The building is officially named the Marriner S. Eccles Federal Reserve Board Building after Franklin Roosevelt's Chairman of the Federal Reserve. It was designed by
Paul Philippe Cret, a Beaux Arts trained architect (Pan American Union building, Detroit Institute of Arts). He later applied modern sensibilities (e.g. reduced ornamentation) to classical forms to come up with buildings like this, the Univ. Texas Main Building and the Folger Shakespeare Library. The style is called Stripped Classicism or Greco Deco(!). If it looks familiar, it was the style used by many of the building built by the New Deal/WPA. It lost popularity, though, when both Nazi Germany and the Soviets under Stalin made it their preferred style.

Thus began Franklin Roosevelt's first broadcast fireside chat, eight days after his inauguration. FDR's response to the banking crisis was codified in the Banking Acts of 1933 and 1935, which centralized the Federal Reserve System -- and led to this building. The design was chosen in a 1935 competition which -- as can be seen -- resulted in the most grounded, solid-looking building imaginable. Very much part of what, it has been plausibly argued, saved American capitalism.