US foreign policy during the Cold War aimed to contain the spread of communism and strengthen America's global influence. In Cuba, US attempts to overthrow Fidel Castro through covert operations like the failed Bay of Pigs invasion scared Castro into allowing Soviet nuclear weapons on the island. This led to the Cuban Missile Crisis and brought the US and USSR to the brink of nuclear war. Tensions were high due to both sides' fear of the other gaining military advantages in regions like Europe and the Caribbean.