Living systems are fundamentally dynamic and adaptive, relying on a constant throughput of energy. They are also, by definition, self-sustaining over the full range of length and time scales (from sub-cellular structures to species considered as a whole). This characteristic combination of constant adaptive flux and emergent persistence requires that the properties of all living systems must, at some level, be cyclical. Consequently, oscillatory dynamics, in which system properties rise and fall in a regular rhythmic fashion, are a central feature of a wide range of biological processes. The scale of biological oscillations covers enormous ranges, from the sub-cellular to the population level, and from milliseconds to years. While the existence of a number of biological oscillations, such such as the regular beating of the human heart or the life-cycle of a unicellular organismis, is widely appreciated, there are many oscillatory phenomena that are much less obvious, albeit no less important. Since oscillations reflect periodic quantitative changes in system properties, their detection and characterisation relies on the quantitative measurement of a system over an extended period. Until recently, such measurements were difficult to obtain at cellular or sub-cellular resolution, and relatively few cellular oscillations had been described. However, recent methodological advances have revealed that oscillatory phenomena are as widespread in cells as they are at larger scales. The papers in this book provide an introduction to a range of both well known and less familiar cellular oscillations, and serve to illustrate the striking richness of cellular dynamics. The contributions focus particularly on elucidating the basic mechanisms that underlie these oscillations. The essentially quantitative nature of oscillations has long made them an attractive area of study for theoretical biologists and the application of complementary modelling and experimental approaches can yield insights into oscillatory dynamics that go beyond those that can be obtained by either in isolation. The benefits of this synergy are reflected in the contributions appearing in this book. That oscillations play central roles in phenomena at all levels of cellular organisation is illustrated by the range of examples detailed in this book. Chapters by Lloyd and by Aon and colleagues describe coherent oscillations in cellular metabolism, a process clearly common to all living cells. Similarly, the cell cycle, discussed by Csiksz-Nagy and colleagues, is a fundamentally cyclical process common to all cells. Rougemont and Naef describe models for circadian rhythms, which are critical in allowing organisms to entrain their cellular activities to imposed daily changes in their environment. The chapters by Lahav and by Momiji and Monk focus on recently-discovered oscillations in cellular response systems, in which the combined requirements of sensitive response and signal termination result in unexpected oscillatory instabilities. Oscillations contribute not only to temporal organisation within cells, but can also direct spatio-temporal organisation in multicellular tissues. Thul and colleagues review the central role played by oscillatory changes in calcium concentration in processes spanning these scales. A striking and well known example of oscillatory patterning at the multi-cellular level is the aggregation of developing cells of the slime mold Dictyostelium discoideum. Loomis discusses the critical role played by oscillatory cAMP signalling in this phenomenon. More recently discovered illustrations of the role of oscillations in spatial patterning are provided by the chapters of Lutkenhaus and Palmeirim and colleagues. Lutkenhaus describes the way in which many bacteria localise their cell division plane through oscillations of Min proteins. Palmeirim and colleagues review oscillatory mechanisms underlying the segmentation of vertebrate embryos. The current resurgence in interest in interdisciplinary approaches to cell and molecular biology (often referred to as Systems Biology) stems in part from the increasing availability of system-wide data on the state of the components of cellular regulatory networks. A limiting factor in these approaches is often the lack of suitable ways of characterising a network state in terms of summary quantitative features. Without such features, it is typically difficult to gain new qualitative insight into the operating logic of all but the simplest networks. In this regard, oscillatory phenomena provide ideal exemplars for systems approaches, since oscillations have clear summary features (such as period, amplitude and phase) that prove invaluable in combining mathematical models with experimental data.