"The transatlantic alliance is likely to become more relevant as new powers rise." That is the conclusion of the report "The Transatlantic Alliance in a Multipolar World" (pdf) by Thomas Wright and Richard Weitz, which was just published by the Chicago Council on Global Affairs.
The most interesting argument in the report is IMHO: "The future appears likely to bring multipolarity without multilateralism. It will thus fall to the United States and Europe to act as a convenor of like-minded countries to ensure that the integrity and effectiveness of the international order is preserved."
This is of great relevance because:
Very recently [...] it has become apparent that the United States and Europe cannot count on emerging powers to bolster the multilateral order. Instead, they often go their own way in pursuit of interests and priorities that are not always in line with what members of the old Western order would like. Brazil, China, Russia, and others may share many of the transnational foreign policy challenges facing the United States, but they do not necessarily share the same priorities or policy prescriptions. They differ in opinion over the likelihood that Iran is seeking nuclear weapons, the extent to which developing countries have a responsibility to cut carbon emissions, how financial imbalances in the global economy should be addressed, and whether or how cybersecurity should be addressed or advanced. Furthermore, the trend is not confined to countries outside of the western order. Turkey, which is a member of NATO and has long sought membership of the EU, has ruffled feathers in the United States with its independent foreign policy, serving as a reminder that Ankara's support should not be taken for granted.
China is described as most responsible for multipolarity without multilateralism:
China's relationship with the West is complex and contradictory. It is an indispensable economic partner but increasingly a political rival whose leaders hold a different vision of international order than those of the United States, Europe, and Asian democracies. This divergence severely complicates prospects for increasing multilateralism in inclusive institutions like the UN.
Europe will be useful again to the United States:
Tensions over burden sharing may continue but new challenges relating to multipolarity are emerging that are better suited to Europe's capabilities and interests. As they face these challenges, the United States and European nations have more shared interests now than at any time since 1989.
The report makes some interesting recommendations for increasing transatlantic cooperation. Though, I am certainly against the proposed NATO Space Command.