Marine connectivity describes the spatial and temporal linkages between separated parts of the global ocean. How different regions are connected, on what timescales, and by which oceanic pathways are important questions for a wide variety of applications. In this talk, we focus specifically on connectivity in the Arctic Ocean. The Arctic is a particularly important part of the global ocean, not least because of the impacts of climate change and loss of sea ice. This presents both opportunities and challenges - for instance, the retreat of Arctic sea ice is increasing interest in exploiting the region for resource extraction and commercial shipping, and changing circulation associated with a warming Arctic may permit invasive species to traverse the ocean. Three cases studies, each related to marine connectivity in the Arctic Ocean, are discussed here. We begin by focusing on the potential impact of oil spills that could occur as a consequence of increased shipping along the Northern Sea route. In the second part of the talk, we explore changing connectivity pathways in the Beaufort Gyre region and their importance in bringing fresh water to the gyre. Finally, we investigate changing Pacific to Atlantic advective pathways in the context of “invasions” of non-native species to the North Atlantic. In each case, a Lagrangian particle-tracking approach was employed. The merits and drawbacks of such an approach are discussed, with the aim of demonstrating that Lagrangian analysis is a powerful tool for understanding a changing Arctic Ocean.