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In neuroendocrinology, mathematical modelling is about formalising our understanding of the behaviour of the complex biological systems with which we deal. Formulating our explanations mathematically ensures their logical consistency, and makes them open to structured analysis; it is a stringent test of their intellectual coherence. In addition, however, modellers are seeking to extend our understanding in new ways, by seeking novel, simple explanations for complex behaviour. Here we discuss some styles of modelling as they have been applied to neuroendocrine systems, and discuss some of their strengths and limitations.