The use of mathematical modelling in understanding and dissecting physiological mechanisms in plants has seen many successes. Notably, studies of the component interactions of the Arabidopsis circadian clock have yielded multiple insights into the roles of specific regulators at the transcriptional and post-transcriptional level. In this article, I review the use of mathematical techniques in dissecting the Arabidopsis clock mechanism, covering first the well-established use of mechanistic models implemented as systems of nonlinear ordinary differential equations. In situations where mechanistic models are not appropriate, I describe how linear time-invariant (LTI) systems, a type of black-box model, can offer quantitative descriptions of biological systems that provide a systems-level understanding without detailed descriptions of the underlying mechanism. A comparison of the two approaches is provided to exemplify when LTI systems modelling might offer advantages for interpreting biological measurements. In particular, formal analysis of large datasets with LTI systems can offer genome-scale inferences, which is of timely relevance as novel experimental techniques are generating increasingly large quantities of data.