The interpretation of physical, chemical and biological phenomena as linear relationships between variables, or as simple functions of the variables, has been a significant scientific and mathematical strategy to their elucidation for centuries. It is often the case that the nature of linearity is to follow mathematical functions, e.g. power, exponential or logarithmic functions, nevertheless the desire to fit data to simple predictable expressions is imbued in every scientist and engineer. From a philosophical standpoint there is no reason to criticize this approach as it allows us to interpret the natural world and has a lofty heritage going back to the classical world. However, non-linear phenomena have been identified in many fields and interpreted as periodic, catastrophic, chaotic or complex involving a variety of mathematical tools for analysis. Benoit Mandelbrot’s now classic book on the fractal geometry of nature and the many subsequent texts, most recently Wolfram’s magnum opus "A New Kind of Science" have raised questions about the nature of reality and the interpretation of observed phenomena. It seems clear that the complexity of dynamic events (on any scale) can rarely be explained by linear interpretations. The rare exceptions are likely to represent a convergence of multiple phenomena giving the appearance of a linear relationship between variables. In fields related to pharmaceutical sciences some texts have been written by pioneers such as Brian Kaye. His eminently readable "A random walk through fractal dimensions" and "Chaos and complexity" were seminal volumes for the editors. Tracing the mathematics of complexity back to the nineteenth century and beyond gives a validity to the search for more accurate interpretations of experimental observations that should impact on the pharmaceutical sciences as significantly as other fields of endeavor. The chemistry and physics literature is replete with papers on complexity from such notables as Ilya Prigogine and Murray Gell-Mann. A broad range of biological phenomena, the most complex imaginable from molecular biology to ecology, are now the subject of complexity analysis. Pharmaceutical sciences encompass the biology, chemistry, physics and mathematics associated with drug discovery, delivery, disposition and action. This text describes a range of topics of importance in the pharmaceutical sciences that indicate a need for a non-linear interpretation if they are to be characterized accurately, understood fully and potentially controlled or modulated in the service of improved therapeutic strategies. It is likely that the future will involve increasingly complex interpretations of data related to drug design and delivery, particularly as our knowledge of the human genome leads inexorably to the potential for individualized therapy. We hope that this text will promote discussion of the varied phenomena leading to pharmacological effect and the complex interactions ultimately resulting in improved disease control and health maintenance.