Circadian clocks involve feedback loops that generate rhythmic expression of key genes. Molecular genetic studies in the higher plant Arabidopsis theliene have revealed a complex clock network. We begin by modelling the first part of the Arabidopsis clock network to be identified, a transcriptional feedback loop comprising TIMING OF CAB EXPRESSION 1 (TOCl), LATE ELONGATED HYPOCOTYL (LHY) and CIRCADIAN CLOCK ASSOCIATED 1 (CCA1). As for many biological systems, there are no experimental values for the parameters in our model, and the data available for parameter fitting is noisy and varied. To tackle this we construct a cost function, which quantifies the agreement between our model and various key experimental features. We then undertake a global search of parameter space, to test whether the proposed circuit can fit the experimental data. Our optimized solution for the Arabidopsis clock model is unable to account for significant experimental data. Thanks to our search of parameter space, we are able to interpret this as a failure of the network architecture. We develop an extended clock model that is based upon a wider range of data and accurately predicts additional experimental results. The model comprises two interlocking feedback loops comparable to those identified experimentally in other circadian systems. We propose that each loop receives input signals from light, and that each loop includes a hypothetical component that had not been explicitly identified. Analysis of the model predicts the properties of these components, including an acute light induction at dawn that is rapidly repressed by LHY and CCAL We find this unexpected regulation in RNA levels of the evening-expressed gene GIGANTEA (GI), supporting our proposed network and making GI a strong candidate for this component. We go on to develop reduced models of the Arabidopsis clock to aid conceptual understanding, and add a further proposed feedback loop to develop a 3-loop model of the circadian clock. This 3-loop model is able to reproduce further key experimental data.