During the past 25 years, the U.S. National Academies of Sciences, Engineering, and Medicine, in collaboration with the Russian Academy of Sciences, have carried out a wide variety of activities to improve understanding of the challenges in containing and reducing ethnic conflicts, violent extremism, and terrorism. Roots and Trajectories of Violent Extremism and Terrorism provides an overview of this cross-ocean program, which has involved American and Russian scientists, engineers, and medical professionals from a large number of government agencies, leading research institutions, think tanks, educational institutions, analytical centers, and consulting and commercial firms in the two countries. This report highlights challenges addressed by the academies over many years that remain of current interest as the U.S., Russian, and other governments continue to cope with old and new forms of aggression that threaten the livelihood of populations at home and abroad.