For many years, the Oxford historian John Roberts has been part of the public face of history in Britain. Originally a student of France, particularly in the 18th and 19th centuries, he progressed to "world history" in the 1980s. His BBC television series The Triumph of the West also became a widely read illustrated book. At a time when a certain pessimism was en vogue, Roberts's ebullient celebration of the persistence of western cultural and ideological, if not politico-military, hegemony, was refreshing. "The story of western civilisation," he argued then, "is now the story of mankind." Had he been given a peerage, the author might have become known, rather like "Lord (Kenneth) Clark of Civilisation", whom he did not otherwise much resemble, as "Lord Roberts of the West".

The author of Twentieth Century: A History of the World, 1901 to the Present is thus no stranger to ambitious projects, and it is not surprising to find him swelling the centennial tide. The field is, however,already a crowded one, with contributions from Martin Gilbert, Mark Mazower and, some time ago, Eric Hobsbawm, to name only the most prominent.Twentieth Century thus has to make up in execution and conceptual coherence for what it lacks in topical novelty. To structure, it is sometimes said, is to leave out. Or, to quote Roberts himself, "the hardest task of the contemporary historian is to discriminate".

His story is, once again, the decline of European power and the fall, rise and transfigurative triumph of the West. Roberts is quite clear from the outset that this means a rigid focus on the winners and innovators of world history, at the expense of everything that "neither illuminates nor contributes to the general themes" of the book. "There is no principle of democracy," he adds candidly, "to ensure equal treatment for states and nations in historical narrative."

In practice, this means that there was no real African or Asian history in its own right at the beginning of the century: "That there was an entity corresponding to the word 'Asia' was a European idea, adopted only by a minority of Asians, not yet an idea most of them would have grasped ... similarly, it was unlikely that many native-born Africans except those that were white would have had any notion that there existed an entity called 'Africa', the name given to the whole continent first by Europeans." There is, in short, no political correctness about this enterprise: "that western values were often better", Roberts assures us, "is of course true".

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Within the parameters it sets itself, Twentieth Century persuades. Roberts shows how the pace of change, which had already quickened considerably in the 19th century, accelerated by leaps and bounds between 1900 and 1999. He takes us through the impact of economic globalisation, the spread of parliamentary government, the rise and collapse of totalitarian alternatives, the clash of the great and superpowers, the apotheosis and disintegration of empires, and the technological revolution that has completely transformed warfare, communications and everyday life. The protagonists are the great states of the West: Britain, Germany, the United States and the Soviet Union (the apostle, as we are reminded, of the western ideology of Marxism). As and when they are invigorated by western ideas of nationalism and economic development, Japan, India and China jostle for attention in Roberts's narrative; the great swathes of Africa that westernisation has largely passed by hardly figure.

All of this is standard fare, but the story is told in a lively and accessible, if slightly uneven style. Some of the writing is very gripping, such as the passages on Stalin and collectivisation. On the other hand, the treatment of key events such as the first and second world wars is comprehensive and competent, but somewhat flat and rehearsed: it is almost as if the author knows that he has little to add on these subjects. Many readers will find this entirely forgivable, for they will be impatient to move on to one of the great strengths of the book, which is the juxtaposition of familiar British and European events with more recondite global forces. One example of this is the account of Middle and Far Eastern development after 1918.

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Inevitably in a work of such scope, there are errors. The Russo-French alliance is usually dated to 1893 not 1892, the Macedonian rising was in 1903 not 1902. President Hindenburg did not die in 1935 but in 1934, the German communist party never obtained more votes than the social democrats before 1933, and the last partition of Poland was in 1795, not 1796. None of these nor other mistakes, however, detract from the overall argument of the book or undermine confidence in the author. Indeed, one is repeatedly struck by the surefootedness of the judgements and the general accuracy of the detail. For example, Roberts's discussion of international relations in Asia since 1950 is informed by the recent archival revelations that followed the collapse of the Soviet Union.

Doubtless, many specialists will cavil at the treatment of their particular area - some German historians might object to the overly negative portrayal of the prospect for parliamentarisation before 1914, or to the slightly monolithic view of the Third Reich, or to the rather schematic way in which the Soviet Union is blamed for the partition of Germany (and Europe). But in the broad scheme of things, these are nuances.

One puzzling aspect of Twentieth Century is the concluding chapter, which is much less of a celebration of western prospects than one might expect, or may even be warranted. At one level, Roberts is clear that American power is more predominant than it was at most points in the 20th century, perhaps even than in 1945. US planners, after all, have now abandoned the concept of "imperial overstretch" in favour of "full-spectrum dominance", the capability to intervene simultaneously across the globe. Yet at the same time, one of the great themes of the book is the decline of European and then western political and military superiority: "it is over"; this is contrasted with the effortless slaughter of Sudanese fanatics at Omdurman in 1898, just before the century began. It is certainly true that the years since 1945 have been the retreat from empire, economic decline, the oil shocks and the American trauma in Vietnam.

Yet much of this ground was made good in the microchip revolution of the 1980s and 1990s, not only economically, but particularly militarily. The disparity between the West and the rest in terms of conventional military potential is now greater than it was in 1970 - and it is increasing. The Sudanese forces at Omdurman, Roberts reminds us, were equipped with steamboats, telegraphs and mines that they did not know how to use. Similarly, the Iraqis in the Gulf and the Serbs in Kosovo might as well have been armed with bows and arrows for all the impact they made on the "smart weapons" of the western coalition. If all this is anything to go by,we are set fair for a 21st century in which the outlook for western values is as promising as it appeared in 1900.

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Brendan Simms is lecturer in international relations, University of Cambridge.