Abstract Transform-margin development around the Arctic Ocean is a predictable geometric outcome of multi-stage spreading of a small, confined ocean under radically changing plate vectors. Recognition of several transform-margin stages in the development of the Arctic Ocean enables predictions to be made regarding tectonic styles and petroleum systems. The De Geer margin, connecting the Eurasia Basin (the younger Arctic Ocean) and the NE Atlantic during the Cenozoic, is the best known example. It is dextral, multi-component, features transtension and transpression, is implicated in microcontinent release, and thus bears close comparison with the Equatorial Shear Zone. In the older Arctic Ocean, the Amerasia Basin, Early Cretaceous counterclockwise rotation around a pole in the Canadian Mackenzie Delta was accommodated by a terminal transform. We argue on geometric grounds that this dislocation may have occurred at the Canada Basin margin rather than along the more distal Lomonosov Ridge, and review evidence that elements of the old transform margin were detached by the Makarov–Podvodnikov opening and accommodated within the Alpha–Mendeleev Ridge. More controversial is the proposal of transform along the Laptev–East Siberian margin. We regard an element of transform motion as the best solution to accommodating Eurasia and Makarov–Podvodnikov Basin opening, and have incorporated it into a three-stage plate kinematic model for Cretaceous–Cenozoic Arctic Ocean opening, involving the Canada Basin rotational opening at 125–80 Ma, the Makarov–Povodnikov Basin opening at 80–60 Ma normal to the previous motion and a Eurasia Basin stage from 55 Ma to present. We suggest that all three opening phases were accompanied by transform motion, with the right-lateral sense being dominant. The limited data along the Laptev–East Siberian margin are consistent with transform-margin geometry and kinematic indicators, and these ideas will be tested as more data become available over less explored parts of the Arctic, such as the Laptev–East Siberia–Chukchi margin.