Mathematical modelling in the natural and engineering sciences is most often dominated by a philosophy of deterministic reductionism. Moreover, many of the ‘simulation' models that emerge from this approach to modelling are very large and so difficult to identify, estimate (i.e. calibrate) and validate in rigorous statistical terms. In this situation, it seems sensible to consider alternative modelling strategies which overtly acknowledge these data-based modelling difficulties and address the very real problems of calibration and validation associated with the dynamic modelling of complex systems from time series data. This paper outlines a Data-Based Mechanistic (DBM) modelling philosophy which attempts to address some of these problems and illustrates its wide-ranging practical utility through seven examples in areas ranging from the natural environment, through ecology and macro-economics to engineering.