In 1990, as a surprised world emerged from the cold war, the Chicago political scientist John Mearsheimer expressed his fears at the passing of the bipolar world order. For the 45 years that the United States and Soviet Union had stalemated each other across the battleground of Europe, he argued, terror of mutually assured destruction had more or less kept the peace. But the fall of the Soviet Union from superpower status might well bring back the “untamed anarchy” of the pre-1945 world.

Mearsheimer was substantially right about what the future held. Through the 1990s, the emergence of ultra-nationalisms tore parts of the old communist world apart. But his analysis of the cold war balance of power was less convincing – a glance back at history reminds us that the cold war was not really a Eurocentric, bipolar conflict. It was, rather, a confrontation that drew in every continent, and in which ambitious state-makers in Africa, Asia and Latin America often played the two superpowers off against each other to maximise material support from both.

Neglecting the dynamics of the cold war in these areas is problematic for many reasons. For one, a politically motivated amnesia may be at work. The sudden collapse of the Soviet world between 1989 and 1991 led some ideologues to assert American moral supremacy: if the Soviet empire imploded due to internal failings, the assumption went, the US must have triumphed due to the overwhelming virtue of its strategies. This conclusion overlooks the cynical brutality with which the US tried to advance its interests. Many of the ongoing tragedies of underdevelopment and violence that trouble Africa, Asia, Latin America and the Middle East today have their roots in conflicts in which the cold war superpowers were once enmeshed.

Another drawback of the bipolar analysis of the cold war is that it ignores the role played by the People’s Republic of China in the conflict. For years, the stereotype of a closed-off, isolated China, shunned by the international community, has dominated popular impressions of the Mao era. Memoirs such as Jung Chang’s Wild Swans described the deranged xenophobia of the early Cultural Revolution. Yet outside the years from 1966 to 1969 (in which the foreign policy of the People’s Republic did indeed self-destruct), Mao’s China poured hard work, money and considerable skill into extending its influence throughout the world.

Some of these initiatives garnered rich political dividends, meaning China enjoyed perhaps its greatest international soft power since the Enlightenment. Mao and his ideas of continuous peasant revolution appealed to leftwing rebels, and to civil rights and anti-racism campaigners in the US, Australia, France, Germany, Holland, Belgium, Italy, Norway and Sweden. Across the developing world, Maoist politics inspired postcolonial nations with ideals such as self-reliance, party rectification and revolutionary spontaneity. The list of those who found in favour of Maoist China is a bewilderingly various one: Quakers, sinologists, French philosophers, Venezuelan pirate revolutionaries, West German dadaist hippies, Congolese feminists, Algerian guerrillas – and Shirley MacLaine, who in 1975 wrote an adulatory account of a six-week visit to China during which she found her way out of a mid-life crisis.

During the cold war, while access to communist documents was very limited (and classification made access to US perspectives at best patchy), historians could tell barely one side of the story – a manoeuvre that George Gaddis Smith memorably described as “one hand clapping”. The explosion in archival access during the past two decades means that there is no longer any excuse for such a narrow focus. The Cold War International History Project has led the way in translating and making available once-secret documents. Visitors to this digital archive can consult sources on topics ranging from the Korean war, the Berlin Wall and the Brazilian nuclear programme to international ice hockey. Between 2003 and 2013, even still-communist China joined the declassification game, releasing thousands of documents archived by the ministry of foreign affairs. Outstanding historians of the cold war inside and outside China – Chen Jian, Li Danhui, Sergey Radchenko, Shen Zhihua, Odd Arne Westad, Yang Kuisong, Xia Yafeng – took advantage. They were right not to hang about: in 2013, a clawback began and in 2014 the archive of the ministry of foreign affairs closed its doors again.

Jeremy Friedman’s meticulously researched Shadow Cold War draws extensively on sources gathered during the brief window of openness to illuminate China’s part in the conflict. His findings underline the crucial importance of the Sino-Soviet split in escalating Soviet and American interference in developing countries.

When China’s new communist government allied itself with the USSR in 1949, a shiver travelled up the spines of western governments. It was, Odd Arne Westad wrote, “the greatest power to challenge the political supremacy of the western capitals since the final expansion of the Ottoman empire in the 16th century”. The alliance immediately created domino-theory panic in the US: “I believe,” noted Eisenhower in 1950, that “Asia is lost with … even Australia under threat. India itself is not safe!”

A decade later, however, this potentially world-dominating alliance unravelled at speed. Denouncing the Soviets as “revisionists” anxious to appease the Americans, Mao and his lieutenants seized every opportunity to sledge the USSR in public and to assert themselves as the true leaders of the world revolution. In 1960, an exasperated (and drunk) Nikita Khrushchev cursed Mao as a pair of “worn-out galoshes”; Mao returned the compliment by calling Soviet policy programmes “long and stinky”. By 1969, China and Russia were edging towards nuclear war.

The Chinese never convinced the main communist parties in Europe that the Soviets were betraying the revolution: Mao’s best conquest in the eastern bloc was Albania. In the developing world, though, Friedman tells a different story. Decolonised nations became a key arena for Sino-Soviet rivalry: a mass of new countries in search of blueprints for state-building and in which Russia and China could promise to build brave new socialist worlds in their own image.

In the early 60s, Khrushchev – pushing his post-Stalin doctrine of “peaceful coexistence” – emphasised economic, material aid to these new countries: more butter, fewer guns. Mao-era China banged a more militant drum, arguing for anti-imperialist revolution and denouncing the Soviet Union for selling out developing nations. The Chinese launched a charm offensive through the 60s: they welcomed a stream of visitors from Asia, Africa and Latin America, and produced broadcast and print propaganda in local languages; they pledged generous aid packages even at the peak of a government-manufactured famine. In so doing, they successfully presented themselves as the champion of small nations. “You are still white,” Africans told the Soviets, “but [the Chinese] are yellow, closer to us.”

Soviet policy in the developing world responded with a shift towards militant, anti-imperialist struggle. The USSR stepped up aid to Algeria and Egypt; it dispatched weapons to Congo and to Palestine. By 1976, the Soviet Union had established itself as the sponsor-in-chief, pledging to liquidate “all remnants of the system of colonial oppression”. It bombarded North Vietnam with rhetorical and material support, to woo it away from its Chinese neighbour. Between the 60s and 70s, therefore, conflicts in Vietnam, Africa and the Middle East were driven not only by tension between the Soviets and the Americans, but also by Sino-Soviet competition for influence.

After the death of Mao in 1976, China pragmatically withdrew from the contest and focused instead on domestic economic reconstruction. Although this move left the Soviet Union the dominant communist power in developing world arenas, it was a pyrrhic victory. Superficially, the second half of the 70s looked like the high point of the USSR’s foreign policy in the cold war, with the accession to power of Soviet-supported regimes in Angola, Ethiopia and Afghanistan. In reality, the USSR was materially overcommitted, while its belligerent rhetoric and the expectations that this created among militant allies such as the Palestine Liberation Organisation jeopardised détente with western countries.

In 1979, the USSR began its disastrous invasion of Afghanistan – a 10-year Soviet equivalent to the Vietnam war that would end in ignominious retreat in early 1989. Through the 80s, the USSR’s military expenditure critically overburdened the state (amounting to a third of its budget). As the citizens of Moscow queued for hours for substandard food, Afghanistan became a public relations disaster for the regime, an emblem of miscalculation and futility. It was, moreover, Soviet intervention in countries including Nicaragua, Angola and Afghanistan that stimulated the “Reagan offensive” in these regions in the 80s: the bankrolling of almost any ally (including Afghan jihadis, the mujahideen) who pledged to fight Soviet influence. The repercussions of this strategy haunt us today.

Friedman makes an impassioned case for the idealism of the Soviet Union’s motives in intervening in the developing world. Since the collapse of Soviet and European communism, this has become an unfashionable argument to make: the system’s economic and political crash has seemingly robbed it of any historical validity. Moreover, the more we have learned from archives and memoirs about the personal behaviour of cold war leaders (Khrushchev’s table-dancing, Mao’s womanising), the more cynical we have become about the politics of the era. But Friedman asserts that the cold war fight for the developing world was about more than empire-building by the USSR, US and China.

Something important is lost, he writes, “if we do not see the second half of the 20th century for what it was: an attempt by many around the world to catch up to the most developed countries and achieve a more just and egalitarian division of wealth on both a domestic and an international scale. The cold war may be over … but the fundamental problem of inequality still remains.”

This is a particularly important lesson from history, as the current migration crisis is partly the result of decades of failed development and of political instability originating in or exacerbated by cold war conflicts.

Shadow Cold War establishes Friedman as a first-rate exponent of the “new cold war history”. Globally minded, enviably multilingual, painstakingly archival, his book poses and answers ambitious questions that educate us about our past and make sense of our present.

• Julia Lovell is the author of The Opium War: Drugs, Dreams and the Making of China (Picador).