The last two or three decades have been a spectacular success for biological research in its reductive mode. Molecular mechanisms, such as the gating of ionic channels and transporters, drug-receptor interactions, control of protein expression and regulation, that could only be treated as ‘black boxes’ by the cell biophysics of the 1960s and 1970s have now been revealed not only in terms of detailed molecular sequences and structures but also, in many cases, in relation to their genetic coding. With the end-point of the Human Genome Project already in sight, it might seem that the excitement will soon be over, leaving our successors to continue the long task of filling in the details and widening the range of applications. That would, however, be a profound misunderstanding both of the nature of the molecular biological approach and of what the next major challenge must be. First, the success of the molecular approach has depended not on a blind and mechanical application of very powerful techniques but rather on using these techniques to answer many of the questions already known to be relevant to functional interpretation at the cell, organ and organism levels. The search for the molecular bases of voltage gating of ionic channels, for example, was regarded as important and became highly focussed because it was already known that such gating plays a crucial role in the functioning of excitable cells. Functional properties identified at higher levels ensured that the sequencing of the relevant proteins was not just molecular stamp collecting. Similar arguments apply to the sequencing of the genome. Hence the demand for the development of what is becoming known as functional genomics. The great majority of genome sequencing cries out for functional interpretation that, at present, we do not have. Second, now that we have so much detailed information at the molecular and cellular levels there is an increasing need to re-integrate this detail into an understanding of how these mechanisms interact in a regulated way to produce normal and pathological functioning. Most physiological functions do not occur at the molecular level. Consider, for example, the origin of cardiac rhythm. There is no molecular oscillator responsible for this. Cardiac pacemaker activity emerges as a property of the interaction of a number of separate protein transporters at the cell level. No single one of these can, by itself, generate rhythm. Similar arguments apply to the study of cardiac arrhythmias, some of which cannot even be studied at the cell level; they require the interactions of large numbers of cells in connected networks. It may well be important also to take into account detailed gross- and micro-anatomy. This kind of interaction is not only complex and highly regulated, it is not susceptible to purely qualitative study. However accurate the information may be about the individual molecular mechanisms, unless this information is represented quantitatively and then integrated into computational work designed to reproduce the interactions, our thinking about function will be largely armchair hand-waving. We can expect that, just as an important functional property like pacemaking only emerges at a higher level, so much of the logic by which living systems are organised and regulated will only become evident by studying the interactions at organ and even whole organism levels. There is a name for the study of this kind of logic of living systems. It is called Physiology which, after all, just means the ‘logic of living systems’. Hence the title of the book (The Logic of Life, Boyd & Noble, OUP, 1993) that celebrated the 1993 International Congress of Physiological Sciences. Yet, just as the sequencing of the genome was not simply called molecular genetics, so there is a need to identify the emerging quantitative physiology that is necessary to take the molecular and genetic information all the way through to physiological function. Some have opted to call the relevant discipline ‘Computational Physiology’. Computation is very necessary, of course, but quantitative studies are not just computational. There is also a need for mathematical and physiological insight. This is the reason why some of us have opted to coin the word ‘Physiome’, as a deliberate linguistic echo of ‘Genome’. There is as yet no firm and settled definition of the ‘Physiome’, but what is certain is that quantitative physiological interpretation will form a large part of its domain. And, just as the Genome concept led to the Genome Project (or was it the other way round?), the idea of the Physiome is leading to the definition of a Physiome Project. This was the subject recently of a small workshop held after the 1997 IUPS Congress in St Petersburg. There is little doubt that the time is ripe for the development of integrative work of this kind to complement the reductive successes of the molecular and genetic approaches. Indications that many others in biological research are thinking the same way are now legion (see, for example, the reports on the Banbury Conference, AW Cowley, The Physiologist, October 1997). The same spirit informed a recent NOVARTIS Foundation symposium held in London on The Limits of Reductionism in Biology (NOVARTIS Foundation symposium no 213, Editors GR Bock and J Goode, Wiley, 1998). Within the Physiome, there will be many sub-projects concerned with individual organs and systems. And foremost amongst these is the Cardiome. The reason is simple. Computational work is far more advanced in the case of the heart than for any other organ. Thus, over 90% of the papers in a recent focussed issue of Chaos, Solitions and Fractals concerned with Nonlinear Phenomena in Excitable Physiological Systems (see volume 5, nos 3/4, 1995) were concerned with the heart. The challenge of integrative work in the case of the heart is not, however, limited to its excitability, exciting though that is! The prospect of integrating all aspects of such an organ, including its biochemistry, mechanics, circulation etc is even more exciting. This was the context in which it was decided to hold a workshop in June 1997 in San Diego entitled “Computational Biology of the Heart: From Structure to Function”. This workshop brought together many of the leading teams in the field and provided an extremely valuable opportunity for interaction between those working on different aspects to discuss how they might be integrated together. Although the question of publication was not an initial motivation, we were delighted when the Editors of Progress in Biophysics and Molecular Biology chose this workshop for the first of their focussed issues. The journal is totally appropriate to this kind of quantitative work. Much of the seminal physiological modelling work in the past has been published in the journal, including notably A. F. Huxley’s first model of the sliding filament mechanism of muscle contraction (Huxley, 1957, see volume 7 of Progress in Biophysics). The articles forming this volume are not the actual presentations made at San Diego. Each author was invited to contribute an article based on the San Diego presentations, but also taking into account the need to make the material accessible to readers of a review journal. We hope and believe that the result is an up-to-date account of the present state of the art in studying the Cardiome, and that it can form the basis on which further and greater progress can be made in the future. The workshop was held at the San Diego Supercomputer Center with the support of the National Biomedical Computation Resource, an NIH national resource that aims to improve access by biomedical scientists to high-performance computing. Workshop co-sponsors included Medtronic Inc. (Minneapolis, MN); Alliance Pharmaceutical Corporation (La Jolla, CA); the UCSD Institute for Biomedical Engineering; the UCSD Institute for Mechanics and Materials; and the UCSD Center for Advanced Computational Science and Engineering. The topics covered at the meeting and which are represented in the articles published here included anatomy and structure, myocardial mechanics and growth, ventricular fluid dynamics and valves, electromechanical interactions, metabolism and energetics, ionic currents and nonlinear dynamics, the propagation of waves and vortices throughout the heart, conduction and defibrillation, and the imaging and visualization of all these processes. Participants also discussed the need to develop a hierarchy of models from the level of the contractile protein and ion channel, to the cell and tissue, and to the organ and organism, as envisaged in the proposed “Human Physiome Project”: complete, integrated, hierarchical models of physiological complexity. The papers published here span scales of biological organization from the genome to the whole body, touching on a diverse range of physiological functions, from chemical and metabolic to mechanical and electrical. The editorial committee for this volume was formed of the three members of the organising committee of the San Diego Workshop (Andrew McCulloch, Jim Bassingthwaighte and Peter Hunter) together with the relevant permanent editor of Progress in Biophysics and Molecular Biology (Denis Noble). This editorial committee took responsibility for the refereeing and editing of the articles.