This paper contains a brief characteristic of the USA-Cuba relations before Obama election as president. The reasons that determined the start of the normalization process are studied. The authors analyze the impact of domestic and international affairs as well as the political shifts in Cuba upon the Obama policy aimed as lifting of the economic blockade imposed on Cuba by the USA, the obstacles and progress of this policy. The features of president Trump policy towards Cuba are unfolded as the reasons to undermine Obama strategy. The possibilities and conditions for a return to normalization of bilateral relations in the nearest future are evaluated.