This volume is about the ancient Greek experience of polytheism, about the relationships between men and gods, between different gods, and also between different forms, versions and characterisations of the same god. The chapters move through the various modes in which divinity operated and was viewed: ‘Many Gods’, ‘The Gods’, ‘One God’, ‘A God’, ‘God’ and ‘Playing the God’.

‘Chaos or order?’ is the question, several times repeated, which governs much of the discussion: should we regard the Greek pantheon as an uncoordinated accretion of divine entities, shaped by isolated needs and circumstances, or does it display kosmos, to use V.'s expression – order, connection, a kind of internal symbolic logic? By asking this question, V. immediately penetrates to the very heart of Greek religion and our approaches to it, and the inquiry has yielded a book of undoubted importance and interest.

‘Coping with the gods’ – with their great number and with the plurality of their manifestations – is something V. sees the Greeks as having to do (see e.g. pp. 85–6 for explicit use of the ‘coping’ terminology), but in a sense it is not the Greeks but we, modern scholars, who find it really hard. The Greeks, in V.'s argument, have instinctive strategies for appreciating diversity without perceiving it in terms of insuperable or damaging paradox. Chief among these strategies is what V. terms the ‘virtuoso winking process’, whereby divergent expressions of (a) divinity are kept apart in thought and perception while simultaneously being linked by a ‘common rhetorical nature’ (p. 436). Modern scholars, on the other hand, discontented with apparent chaos, have frequently tried to obliterate contradiction and to smooth out Greek religion into a coherent and harmonious whole. This, as V. argues, is mistaken, for it obscures the inherent importance of disharmony in Greek religion, and badly distorts the realities of the ancient religious experience. As V. puts it on p. 87: ‘The historian's task is to complicate, not to clarify’; with this claim he is, as he acknowledges, building on his own existing work, the two volumes of Inconsistencies in Greek and Roman Religion (1990 and 1993).

The clarifiers are given their figurehead: Vernant, the father of the Structuralist approach which typifies the search for thematic coherence in myth and ritual. A great deal of the book's argument is framed within the methodological opposition of Vernant and Burkert, who at times come themselves to seem like one of the symbolic bipolarities so beloved of Structuralism and so disliked by V. (p. 145: ‘binary disease’, ‘bipolar infection’, ‘plague’). This reflects the fact that this is not just a book about Greek religion, but a book about books about Greek religion. As V. admits (pp. 5–6), during its creation scholarship in the field has in fact started to evolve independently beyond the approaches he criticises, especially in the recognition of the importance of establishing local religious contexts, and Structuralism is by no means an uncontested orthodoxy. It is worth noting R. Parker's Polytheism and Society at Athens (2007) as further evidence of fresh recent attempts to gain a nuanced picture of the working of the ancient pantheon; plainly V.'s volume is in some senses swimming with the tide rather than against it.

So is the polemic of this book still valuable? Very much so, for one reason in particular. Among its most valuable contributions is to offer a compromise between two equally unsatisfactory positions: on the one hand, rootless and meaningless universalism, detached from the experience of any real Greek; on the other hand, a dour and disingenuous insistence that religion can only be studied on the micro-level, within one text, one site, one click of the camera's shutter. V. breaks out of this fruitless non-choice by reasserting the validity of composite characterisation: Greek gods were formed of a rich amalgam of materials, and the way in which they were seen and regarded by individuals would have been coloured by this richness. The error for scholars lies not in envisaging such composite characterisations, but in trying to purge them of contrasts.

If I have any criticism of this argument at all, it is a very slight one. I should have appreciated a little more clarity about the relationship between two overlapping but somewhat different phenomena which are identified: situations where different literary works give different characterisations of a deity, but may be taken together as ingredients of the composite picture; and cases where a single source deliberately represents a deity in terms of ambiguity and contrast. The chief example of the latter is Hermes, who repeatedly emerges as a god used by authors (and vase-painters) to express uncertainty and paradox, and to challenge the solidity of the divide between gods and men. This is rather special, and perhaps deserves to be distinguished more clearly from cases where we extrapolate ancient ambivalence by comparing different texts which give divergent depictions but are not internally ambiguous.

Parallel to his unflagging awareness of existing scholarship, V. is self-conscious throughout with regard to his own approach and its implications. Though the rhetorical manifestation of this self-consciousness occasionally irks, on a more important level it is what allows V. to avoid the pitfalls inherent in such a wildly ambitious book. For ambitious it is, especially in the enormous range of material brought together, divergent in date and nature, whose juxtaposition he handles with admirable deftness. In fact, in one regard one might wish for more, rather than less: the discussion of Hermes in vase-paintings throws into relief the curious lack of visual material in the rest of the work. This does not constitute an error (the book makes no claim to be systematically comprehensive) but the effectiveness of the discussion of the Hermes imagery makes one wish he had taken this approach more often: after all, images – on public buildings and domestic objects – would have made up a substantial component of how a Greek experienced his gods from day to day.

Apart from this one patch of neglect, however, the compendious nature of the book is striking; while maintaining a flexible hold on its central tenets, it encompasses an array of tangential themes which ensure that it is not of narrow and limited value to the historian of religion alone. For example, the discussion of Herodotus on pp. 179–87 will interest those working on ancient historiography, and Chapter 6 makes a substantial contribution to our understanding of Hellenistic power-politics. There is a kind of generosity about the scope of the work: the appendices, for example, would have provided a run of substantial articles had V. chosen to exploit them as such. Their inclusion in the book, however, suits its refusal of the uniform, both in our appreciation of the ancient world and in its own construction of scholarly narrative. A simple narrative would, of course, have been wholly inappropriate in a book about the terrible danger of simplicity.

Densely textured though it is, however, the volume is never dry. In addition to the inherent fascination of the material, its style is unfailingly lively and frequently amusing (for example, the peevishness of the defence of long footnotes in the introduction is disarmed by the good-humoured afterthought in p. 20 n. 29). The engaging tone of the main narrative may in part derive from the book's origin as a series of lectures (the Sather Lectures, given at the University of California at Berkeley in 1999). Most importantly, however, this is the work of an author who loves his subject, so much so that he sees himself as in some ways its rescuer from the clutches of those who seek to confine the Greeks within ‘late modern monolithical and mono-paradigmatic dogmas’. An important aim, and one amply fulfilled.