Vladimir Putin’s plunge into Ukraine has turned America and Russia into mortal enemies even though they’re not firing directly at each other. Rather, America, as the leading member of the North Atlantic Treaty Organization, is pouring billions of dollars into a classic proxy war against the Russians. 

NATO, led by America, is fighting Russia through the medium of the Ukraine forces that in addition to halting the Russian advance have forced the Russians into a humiliating retreat from regions they had overrun in the opening weeks after their invasion.

President Putin’s stubborn drive to try to bring Ukraine under Russian control as it had existed in the era of Soviet rule under Josef Stalin represents a reversion to the worst period of the Cold War. It’s as though Mr. Putin hopes to rebuild the Soviet empire.

The Russ strongman believed, as the invasion began, that his forces could regain control of Ukraine in days or weeks. The Russians quickly controlled the eastern Donbas region and had long since seized Crimea, the southern peninsula that Stalin’s successor, Nikita Khrushchev, had earlier ceded to Ukraine.

Now all the Russians have to do, in Mr. Putin’s view, is to complete the conquest of a land that had once been under Soviet rule and, in an earlier period, a possession of Tsarist Russia. Yet Mr. Putin made two essential miscalculations.

First, he underestimated the will of Ukrainian forces under President Zelensky, a former television comedian who had been elected president by a wide margin, to marshal widespread support for the defense of Ukraine.

Second, he failed to foresee that President Biden would be willing to offer up the costly resources for the Ukrainians to keep fighting. Mr. Biden’s willingness to provide the weapons the Ukrainians desperately needed also encouraged other NATO members, notably Britain, to invest in Ukraine’s defense.

Messrs. Biden and Putin have stopped short — at least so far — of turning the Ukraine invasion into a Russo-American and, ultimately, a nuclear war. Mr. Biden’s reluctance to go directly into combat with the Russians means that he has refused pleas to declare the skies over the country as a “no-fly zone.”

To enforce that zone, warplanes would have to pursue Russian planes and bomb Russian bases. The result could be a rapid escalation into World War III. Plus, Mr. Putin’s allusion to Russia’s nuclear capabilities has inspired fears that he might initiate a nuclear war that could envelop Europe.

It’s hard to believe, however, that he would go beyond merely reminding NATO that Russia is the world’s leading nuclear power, with a stockpile far bigger than that of the Americans, the second-ranking nuclear power, and that someday the conflict could expand. 

The vagueness of his rhetoric leaves the impression that he merely wants to put a scare into his enemies without seriously following up, as might happen in a far wider armed confrontation.

Relations between America and Russia, however, have descended to their lowest point since the depths of Stalin’s rule. Mr. Putin has threatened to break off relations entirely as a result of sanctions. Mr. Biden has named a new ambassador to Moscow, Lynne Tracy, to replace John Sullivan, who has just retired.

Russia has attempted to assert its economic power by withholding shipments of natural gas to Germany and other countries, but its own economy is suffering under the unexpected setbacks in Ukraine. Mr. Putin has asserted his determination to renew the offensive, but his own grip on power may be wobbling.

The war, in any event, is far from over. It’s sure that Russia will be on the offensive again, seeking to recover the land from which it retreated. Russia’s historic grip over the region runs deep. 

Long after the tsars controlled Ukraine from afar, Stalin starved Ukrainians in the 1930s, subduing independent-minded farmers, stealing their crops in order to feed Russians in the Soviet heartland. The result was the deaths of several million Ukrainians, a national tragedy engraved in the psyche of latter-day Ukrainians as they fight valiantly against the rebirth of Russian rule.

The fear is that Mr. Putin will also want to recover other former Soviet satellites, including the Baltic states of Latvia, Lithuania, and Estonia, all NATO allies and members of the European Union. 

Russian setbacks in Ukraine have been so unexpected and severe, however, that Mr. Putin may be worrying about his own survival as a revanchist leader with fantasies of the days of Russian glory of past centuries.