This thesis addresses blood pressure regulation from a mathematical modelling perspective. Blood pressure is controlled via a number of different negative feedback mechanisms. The baroreflex loop is the most dominant of these mechanisms for short-term control of blood pressure, and soft-limiting nonlinearities inherent in this loop, are thought to give rise to a slow limit cycle oscillation in blood pressure at 0.1 Hz in the human. Measurement of the strength of this slow oscillation has been proposed as the basis for the development of a diagnostic test of cardiovascular dysfunction or disease. Due to this hypothesis, extensive effort has been invested in measuring the strength of this slow oscillation in blood pressure in a range of physiological and pathophysiological conditions. However, the momentum of this research has continued with little consideration given to the fundamental cause of this oscillation. The means of genesis of the slow oscillation in blood pressure is the major focus of this research, and a mathematical modelling approach was undertaken to analyse the nonlinear mechanisms that give rise to this slow oscillation. The theory that the slow oscillation in blood pressure results due to the feedback nature of the baroreflex loop, and is a limit cycle oscillation established by the nonlinear elements in this feedback loop, is initially investigated by the analysis of blood pressure data recorded during different physiological conditions in which the strength of the slow oscillation in blood pressure was observed to change. Nonlinear time series analysis methods were used to investigate for the existence of a limit cycle oscillation in blood pressure, and so that insight may be attained into the effects of changes of the nonlinear characteristics on the slow oscillation. Following this, changes in the strength of the slow oscillation were investigated, again during different physiological conditions, via a model of baroreflex control of the vasculature. Complications to this analysis, due to the difficulty of developing an analytical describing function representation of the nonlinear sigmoid characteristic inherent to the baroreflex, led to the investigation of a range of describing function approximation methods for the sigmoid nonlinearity, which permeates the cardiovascular literature. A nonlinear model of the complete baroreflex, including the cardiac branch, which has often been ignored, was developed. The ability of the model to replicate the slow oscillation in blood pressure was assessed. A significant role for the heart in the development of the oscillation was identified. An analytical analysis technique was developed to investigate the significance of the different pathways of the baroreflex involved in the genesis of the slow oscillation. This analysis resulted in the development of conditions under which a sustained limit cycle oscillation can occur. In particular the role of mean levels of cardiac output and vascular resistance, previously thought to be relatively unimportant, in establishing and maintaining sustained oscillations, was highlighted. The ultimate aim of this research was to develop the understanding of the mechanisms involved in the genesis of the slow oscillation, and thereby, to assist in the development of a diagnostic test based on non-invasive measurement of the slow oscillation in blood pressure.