This chapter reviews the debate on the decline of US hegemony; it is divided into six sections: the first one sketches the debate on the decline of the United States as a world hegemonic power; the second takes a step back and looks at the initial conditions around which the debate revolved. The third section considers the means through which Washington achieved hegemonic status in the aftermath of World War II and was able to sustain it during the Cold War, according to different approaches. This account in turn serves to re-examine, in the fourth section, the phases the debate on the decline of US hegemony has gone through since the 1970s; here the discussion focuses on the Western Hemisphere, and particularly on Latin America, in order to introduce the theoretical debate to the region. Section five frames the discussion in terms of anarchy versus hierarchy, as it argues that the underlying theme in the various stages of the debate is the type of order that exists in international politics. The last section recaps the discussion presented.