The article looks into the current state of Russian-American relations, which have entered a new period after the events of 2014 in Ukraine. Many experts compare the situation with the Cold War, but the actual state of international relations is very different. Russia and the U.S. are no longer ideological opponents; their relations are no longer decisive to global affairs. U.S.-Russian relations have remained highly competitive in nature since the end of the 19-th century. Both countries employ contradictive ways of national expansion and providing national security. They also have differing values, which define competing forms of exceptionalism and universalism. This leads to incompatibility of their views on the world order: Russia aspires to a Westphalian world with spheres of influence rules by the great powers united by mutual interest and understanding, whereas the U.S. prefers an open rules-based order with no spheres of influence. Russia is also deeply concerned about America's inclination towards a unipolar world, dominated by the United States. In the short term, the main challenges in the bilateral relations will remain European security, the Middle East, strategic stability and sanctions. In the long term they will be shaped by certain global trends, such as power shift from the West to the East, technological advancement, raise of transnational challenges, such as extremism, international crime, proliferation of dangerous technologies, climate change and the raise of the multipolar world, with the U.S., China, Russia, India, Japan, and some European powers as key players. The key challenge for Russia remains its lagging behind the world leaders in crucial areas of development. For the U.S., it is its tiredness of the burden of global leadership. In the future, America will likely to perceive itself as just one of the world leaders. Its grand strategy will remain U.S. preeminence in the Western hemisphere; neither Europe nor East Asia nor the Middle East dominated by a hostile power; safe maritime trade routes. Russia's grand strategy is likely to include Russian preeminence in the former Soviet space; the prevention of the emergence of a unified Europe balancing economic ties between Europe and East Asia; the erection of a reliable barrier against Middle Eastern extremism; and resistance to the rise of a single dominating power in global affairs. There is a strong need for U.S.-Russian cooperation in dealing with the rise of China, European affairs, the Middle East, the Arctic as well as strategic stability issues. The future world order is likely to shift towards a concert of great powers, preferred by Russia.