HMEIMIM AIR BASE, Syria—North from Syria, along the borders of Eastern Europe and rounding the Arctic Circle to the east, Russia has built a ring of air defenses that threaten the reach of the U.S. military, forcing Washington to rethink its place as the world’s undisputed air power.

Russia’s S-400 antiaircraft missile system, a nettlesome and potentially deadly aerial shield, is changing the calculus of the U.S. and its allies in potential hot spots, beginning with its deployment in Syria.