The United States, according to official U.S. national security statements and an avalanche of commentary since about 2016, is engaged in a long-term strategic rivalry with China and a lesser — but still critical — rivalry for influence with Russia. Many U.S. strategy documents refer to the concept of strategic competition, but the core idea — and increasingly the reality — of these relationships matches the classic historical concept of a great power rivalry. These rivalries, especially with China, promise to define U.S. foreign policy and national security challenges for decades. Yet most assessments of these rivalries tend to ignore the critical question of outcomes. This report is part of a larger project on the societal sources of national dynamism and competitive advantage. This research aims to identify historical modes of strategic success and failure in great power rivalries that offer lessons for the United States. The authors define categories of success and failure (in terms of such variables as control over territory, relative power, victory or defeat in war, international legitimacy, and social stability) and present detailed case studies on specific historical examples that are associated with success and failure. They also discuss the implications of the typologies of both kinds of outcomes for the rivalry with China.