The human cardiovascular system (CVS) is a highly complex mechanism. Signals derived from it are difficult to analyse because they are time-varying, noisy, and of necessarily limited duration. The application of techniques drawn from nonlinear science has, however, yielded many insights into the nature of the CVS, and has provided strong evidence for a large degree of determinism in the way it functions. Yet there is compelling evidence that random fluctuations (noise) also play an important role. The extent to which the CVS can be modelled as a stochastic nonlinear dynamical system is reviewed, and future research and possible applications based on this perception are discussed.