President Barack Obama explained his historic reversal of half a century of US antagonism towards Cuba as necessary because of the failure of the policy of hostility pursued by his ten predecessors. But the old policy’s failure was not new, and thus was not, in itself, an adequate explanation for the dramatic shift. This article uses theories of agenda-setting, policy failure and policy change to explain the persistence of the US policy of hostility from 1959 to 2014 and the policy change announced by President Barack Obama in December 2014. Four structural factors account for the continuity in policy and, as a result of gradual changes in those factors, the eventual policy shift. They are: the security threat Cuba posed to the United States during the Cold War; the political influence of the Cuban American community; the diplomatic cost to Washington, especially in Latin America, of maintaining the status quo; and domestic changes under way in Cuba.