There are many physical processes within our world which scientists aim to understand. Computer models representing these processes are fundamental to achieving such understanding. Bayes linear emulation is a powerful tool for comprehensively exploring the behaviour of computationally intensive models. History matching is a method for finding the set of inputs to a computer model for which the corresponding model outputs give acceptable matches to observed data, given our state of uncertainty regarding the model itself, the measurements, and, if used, the emulators representing the model. This thesis provides three major developments to the current methodology in this area. We develop sequential history matching methodology by splitting the available data into groups and gaining insight about the information obtained from each group. Such insight is then realised through a wide array of novel visualisations. We develop emulation techniques for the case when there are hypersurfaces of input space across which we have essentially perfect knowledge about the model’s behaviour. Finally, we have developed the use of history matching methodology as criteria for the design of physical system experiments. We outline the general framework for design in a history matching setting, before discussing many extensions, including the performance of a comprehensive robustness analysis on our design choice. We outline our novel methodology on a model of hormonal crosstalk in the roots of an Arabidopsis plant
