From the English team that brought you The Arrow of Time (1991), more on the general theme that the most interesting things in life are nonlinear, asymmetric, chaotic, and complex--in short, not user-friendly, but perhaps computable. Coveney, a senior research scientist at the Schlumberger Cambridge Research Laboratory, and Highfield, the Daily Telegraph's science editor, have combed the avantgarde labs from hither to von to come up with a review of virtually (no pun intended) all that's current and choice in modeling ""complexity."" The term, not easily defined, speaks to the interactions of subparts of systems that yield processes and outcomes that are greater than the sum of the parts. The weather, chemical reactions, population dynamics, ""emergent"" brain phenomena such as consciousness--all are complex phenomena challenging scores of researchers armed with the latest versions of computer-based cellular automata, neural networks, artificial intelligence, and so on. This is heady stuff, not easily absorbed in the short summaries that describe this or that particular model. On the other hand, chapters that sketch the background and the seminal ideas from Charles Babbage to Alan Turing, Kurt G"del, and John von Neumann are useful contexts for the vast array of examples the authors provide. When they do elaborate a model (for example, the use of infrared data to model at what point in time the ingredients of a cement slurry ""set""), they are very good indeed. It is suggested that readers approach the last chapter first: It captures the authors' grand vision of what might be possible (e.g., molecular-based computers and a universal mind) but sounds a proper warning as well on what folly can also be wrought. Overall, their enthusiasm marks the authors as true believers that the efforts of mankind (yes, mostly men) to take on complexity, achieving both beauty and order, will succeed.