This thesis introduces a comprehensive atlas of behaviour in the iron-catalysed Belousov-Zhabotinsky reaction across a wide parameter space, under both stirred and unstirred conditions, encompassing variations in the concentrations of sulfuric acid, malonic acid and sodium bromate. All stirred reactions were monitored by UV-vis spectroscopy enabling the definition of concentration-dependent transitions in behaviour including those to chaotic oscillation. A programme was generated to quantify spirals observed in the unstirred reaction. This expanded on the work of Müller et al. by increasing the length of time that such spirals had been monitored. There was good agreement between their experimental results and those set out in this thesis, which shows the transition from normal spiral wave behaviour to a final steady state. The work on spiral waves also includes the first use of a statistical image-based method for identifying changes in chemical wave behaviour with time. Attempts were made at producing a model for the iron-catalysed Belousov-Zhabotinsky reaction using a swarm intelligence algorithm having identified key reactions involved in modifying the reaction behaviour based upon the Marburg-Budapest-Missoula model. A further comparison between this model for the cerium-catalysed reaction and the chemical component of the Kyoto Encyclopaedia of Genes and Genomes database demonstrated that study of such small scale systems is applicable to a larger scale biochemical network.