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In the post-genomic era, our attention is turning to how to assemble the "pieces of the jigsaw puzzle" together into realistic and dynamic models of complex biological systems, and to try to understand what may be the fundamental principles governing how cells, organs and organisms have come about, and can evolve. One might say that this is a search for a biological "theory of everything"! In this talk, we examine some possible such principles, and how they could be used to infer computational models from experimental data -- a discipline now becoming known as "systems biology." Systems biology poses many interesting experimental and computational challenges. By examining several illustrative examples we hope to show how it might be possible to predict the behaviours of complex biological systems. The examples we choose are: (a) genetic and protein interaction networks at the intracellular level (b) simulation studies of whole organs, which show how models at the cellular level can be integrated into complete and useful models of entire systems such as the heart. We also briefly examine some of the implications of systems biology for drug discovery, human health and the environment.