The neuroendocrine systems of the hypothalamus are critical for survival and reproduction, and are highly conserved throughout vertebrate evolution. Their roles in controlling body metabolism, growth and body composition, stress, electrolyte balance and reproduction have been intensively studied, and have yielded a rich crop of original and challenging insights into neuronal function, insights that circumscribe a vision of the brain that is quite different from conventional views. Despite the diverse physiological roles of pituitary hormones, most are secreted in a pulsatile pattern, but arising through a variety of mechanisms. An important exception is vasopressin which uses bursting neural activity, but produces a graded secretion response to osmotic pressure, a sustained robust linear response constructed from noisy, nonlinear components. Neuroendocrine systems have many features such as multiple temporal scales and nonlinearity that make their underlying mechanisms hard to understand without mathematical modelling. The models presented here cover the wide range of temporal scales involved in these systems, including models of single cell electrical activity and calcium dynamics, receptor signalling, gene expression, coordinated activity of neuronal networks, whole-organism hormone dynamics and feedback loops, and the menstrual cycle. Many interesting theoretical approaches have been applied to these systems, but important problems remain, at the core the question of what is the true advantage of pulsatility.