The U.S. innovation environment relies on complex and diverse cross-sector collaborations and multi-stakeholder coalitions, and international relationships are critical to this mix of partnerships. For decades, top students, researchers, and entrepreneurs from around the world have sought to come to the United States, drawn by a system that values innovation, creativity, and an open exchange of knowledge and talent. Prioritizing these values and partnerships has fostered U.S. science and technology leadership for decades. At the same time, countries are investing heavily in their own research and development capabilities, while U.S. federal spending has remained stagnant as a percent of gross domestic product. Economic and national security concerns have impacted some aspects of America's collaborative spirit and openness. In February and March 2021, the Government-University-Industry Research Roundtable (GUIRR) of the National Academies of Sciences, Engineering, and Medicine convened its membership to examine the opportunities and challenges of global cooperation and partnerships in the pursuit of U.S. science and technology leadership. Over the two months, GUIRR hosted six virtual workshops on elements of U.S. science and technology policy related to international engagement and competition. Topics included challenges to U.S. science and technology leadership; the intersection of science, foreign policy, and development assistance; public-private partnerships to foster innovation; the value of international research collaboration; U.S. leadership in international standards bodies; and attracting and supporting international students and researchers in the United States. This document summarizes the presentations and discussions at the six workshops.