The Arctic faces multiple pressures including climate change, shifting demographics, human health risks, social justice imbalances, governance issues, and expanding resource extraction. A convergence of academic disciplines—such as natural and social sciences, engineering and technology, health and medicine—and international perspectives is required to meaningfully contribute to solving the challenges of Arctic peoples and ecosystems. However, successfully carrying out convergent, international research and education remains a challenge. Here, lessons from the planning phase of a convergence research project concerned with the health of Arctic waters developed by the Arctic Science IntegrAtion Quest (ASIAQ) are discussed. We discuss our perspective on the challenges, as well as strategies for success, in convergence research as gained from the ASIAQ project which assembled an international consortium of researchers from disparate disciplines representing six universities from four countries (Sweden, Japan, Russia, and the United States) during 2018–2020.