Many were willing to overlook Stalin’s Terror for the sake of anti-fascist unity. But Communism’s second coming in the late ’30s and early ’40s did not long outlast the defeat of fascism. As the Cold War intensified, Communism’s identification with Soviet empire in Eastern Europe compromised its claim to be a liberator. In Western Europe, a reformed, regulated capitalism, encouraged by the United States, provided higher living standards and welfare states. Command economies that made sense in wartime were less suited to peace.

But if Communism was waning in the global North, in the South it waxed. There, Communists’ promises of rapid, state-led modernization captured the imagination of many anticolonial nationalists. It was here that a third red wave swelled, breaking in East Asia in the 1940s and across the post-colonial South from the late 1960s.

For Geng Changsuo, a Chinese visitor to a model collective farm in Ukraine in 1952 — three years after Mao Zedong’s Communist guerrillas entered Beijing — the legacy of 1917 was still potent. A sober peasant leader from Wugong, a village about 120 miles south of Beijing, he was transformed by his trip. Back home, he shaved his beard and mustache, donned Western clothes and evangelized for agricultural collectivization and the miraculous tractor.

Revolutionary China only strengthened Washington’s determination to contain Communism. But as America fought its disastrous war in Vietnam, a new generation of Marxist nationalists emerged in the South, attacking the “neo-imperialism” they believed their moderate socialist elders had tolerated. The Cuban-sponsored Tricontinental Conference of African, Latin American and Asian socialists in 1966 introduced a new wave of revolutions; by 1980, Marxist-Leninist states extended from Afghanistan to Angola, South Yemen to Somalia.

The West also saw a Marxist revival in the ’60s, but its student radicals were ultimately more committed to individual autonomy, democracy in everyday life and cosmopolitanism than to Leninist discipline, class struggle and state power. The career of the German student firebrand Joschka Fischer is a striking example. A member of a group named Revolutionary Struggle who tried to inspire a Communist uprising among autoworkers in 1971, he later became a leader of the German Green Party.

The emergence from the late ’70s of an American-led order dominated by global markets, followed by the fall of Soviet Communism in the late ’80s, caused a crisis for the radical left everywhere. Mr. Fischer, like many other 1960s students, adapted to the new world: As German foreign minister, he supported the 1999 American bombing over Kosovo (against the forces of the former Communist Serbian leader Slobodan Milosevic), and he backed Germany’s welfare cuts in 2003.

In the South, the International Monetary Fund forced market reforms on indebted post-Communist countries, and some former Communist elites proved eager converts to neoliberalism. Only a handful of nominally Communist states now remain: North Korea and Cuba, and the more capitalist China, Vietnam and Laos.