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This is the fourth edition of a work that first appeared in 1976 and is of greatest interest for the revisions made since the third edition was published in 1992. Most of these occur in the last section, but it is still useful to read the coverage of earlier centuries to observe the judicious character of the late J. M Roberts' (who died last week) judgements. For example, he argues that, in assessing the theory and practice of medieval intolerance, it is necessary to remember that the danger in which society was felt to stand from heresy was appalling.

He also points out that persecution did not prevent the appearance of new heresies and suggests that "heresy was, in one sense, an exposure of a hollow core in the success which the Church had so spectacularly achieved". His skill is seen in his adeptness at making general points while maintaining an awareness of the difficulties of this task. Thus, for Southeast Asia and Indonesia in the period 1850-1914, he notes: "Few generalisations are possible about so huge an area and so many peoples and religions. One negative fact was observable: in no other European possession in Asia was there such transformation before 1914 as in India, though in all of them modernisation had begun the corrosion of local tradition."

As also in his discussion of the 18th century, Roberts balances his particular account of the last decade with a sense of long-term perspectives derived from what he terms historical inertia. In his view, historical forces moulding thought and behaviour were laid down centuries before ideas such as capitalism and communism were invented, a valid point but one that may underrate the disruptive consequences of urbanisation and industrialisation over the past two centuries. Roberts' sense of continuity leads him to be sceptical about the notion of fundamental change stemming from September 11 2001. He also suggests that temperament affects the judgement of recent or contemporary events, and thus the character of a world history that lasts to the present.

Roberts has maintained the western focus of previous editions, although China and India receive due attention. The failure of India to become a world power is discussed, as is what Roberts presents as the slow and patchy arrival of modernity. This he presents in terms of the entrenched nature of the Indian past "with all that means in terms of privilege, injustice and inequity". This approach to history, in terms of a tension between modernity and the past, has a Whiggish tinge. Chinese developments in the 1990s receive insufficient attention, but Roberts notes increases in organised crime and rural unrest, and draws attention to the failure to give institutional protection to liberalising policies. The environmental impact of Chinese developments would have repaid more attention.

The early history of "black Africa" and pre-Colombian America are only sketched. Roberts' justification is that they did not play a major role in shaping the world. He claims that "although we properly still take time and trouble to gaze at and study the fascinating sites of Yucatan, to ponder the ruins of Zimbabwe or wonder over the mysterious statues of Easter Island, and intrinsically desirable though knowledge of the societies that produced these things may be, they remain peripheral to world history". Instead, he suggests that the world's politics are for the most part organised around concepts that were originally European, just as science originating in Europe is central to the world's intellectual life and is seen by Roberts as bringing a great extension of practical freedoms. This approach underplays the interest and importance of non-western histories. Furthermore, even from Roberts' "western-centric" perspective, his book could have been amplified by a greater stress on the interdependency of western and non-western cultures and developments. That emerges as a theme in The Human Web: A Bird's Eye View of World History by J. R. and W. H. McNeill, a work that is also very good at considering humans as a species.

Roberts offers a qualified account of recent US power, suggesting that the unresolved nature of ethnic and social problems are an important question mark against American achievement. He argues that the US squandered the possibilities of world leadership at the end of the cold war, and draws attention to ambiguities in American policy, especially in relations with the United Nations and in the Middle East.

The book closes by emphasising the interconnected trends of a growing acceleration of change, a growing unity of human experience and the growth of human capacity to control the environment. As Roberts points out, however, the basis of shared experience - seen, for example, in the spread of urbanisation and urban culture, disease and cars - is only secondarily a consequence of any conscious commitment. Furthermore, while there is little doubt of the human capacity to damage the environment, control is less apparent. Indeed, serious doubt has arisen about the capacity of society to tackle problems. The end result of expansion has been seen not only in particular drawbacks (for example, dams lessening the ability of rivers to flush out deltas and estuaries), but, more generally, in a pernicious assault on an interdependent global environment.

Unlike the McNeills, Roberts takes a generally positive note, arguing that humanity faced the challenge of the ice ages with far poorer resources than those it can deploy against climatic change today: "The human being remains a reflective and tool-making animal and we are still a long way from exhausting the possibilities of that fact." His coverage of environmental history is too brief, but a testimony to his skill and judgement is that I wish he had said more. This is not a short book but it is first rate.

Jeremy Black is professor of history, University of Exeter.