This vision paper outlines the challenges and opportunities within the four key research areas and synthesizes the outcomes of discussions that have emerged through this transatlantic dialogue. In doing so, it seeks to provide actionable recommendations to guide future research initiatives, inspire technological progress, and strengthen the EU-US partnership in distributed computing and swarm intelligence. By addressing these shared priorities, this paper envisions a future where innovation and cooperation across continents catalyze the emergence of transformative technological advancements in distributed computingand swarm intelligence.