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This review employs academic and policy literature to gage the relative importance and concerns associated with the main challenges facing the management of transboundary river basins: increasing pressures; management and policy that has not kept pace with a broadened set of actors; the influence of climate change; and the politics of reconciling political borders and basin boundaries. The persistence of the supply‐side management philosophy within current political economies is also reviewed, along with infrastructure and institutional responses to the challenges (e.g., IWRM, dams, treaties). An analytical frame developed from the review is applied to three basins where there has been successful, considerable, or no effort at transboundary basin management: the Rhine, the Nile, and the Euphrates. International politics and national self‐interest are found to be the key challenge facing international basins, though each of the challenges is interconnected and should be considered in combination. If transboundary basin management is to confront the challenges successfully, it should develop along two paths: away from a supply‐side management paradigm toward adaptive management, and away from sovereignty and unilateralism to multilateralism. While infrastructure built under a paradigm of reducing uncertainty is found to reduce the adaptation options set, adaptive management that can make the most of the increasingly diverse governance and confront the supply‐management philosophy is seen as best‐suited to meet future challenges. The disabling effect of sovereignty and international politics may best be addressed by confronting resistance of the promotion of ‘shared sovereignty’ and fair water‐sharing. WIREs Clim Change2013, 4:331–349. doi: 10.1002/wcc.228