Sir William Paton was one of Claude Bernard’s great admirers (Paton, 1976). It is easy to see why. His book in 1865 (Bernard, 1865, 1984) was a milestone in defining the nature of physiology, and in establishing its experimental basis. It greatly influenced the foundation of The Physiological Society in 1876 (Noble, 1976). It is much less well-known that Bernard also foresaw the need for theoretical as well as experimental physiology. He wrote “the application of mathematics to natural phenomena is the aim of all science” (Cette application des mathématiques aux phénomènes naturels est le but de toute science), though he did also acknowledge that, in 1865, it was far too early to achieve that in physiology. My lecture will seek to show that computational physiology is now succeeding in establishing the basis for what Claude Bernard anticipated (Crampin et al., 2004), and that it is an essential component of physiology’s contribution to the rapidly-growing field of Systems Biology. Physiology has an important contribution to make since it works at all levels of biological organisation. In this lecture I will outline some principles of Systems Biology from a physiologist’s perspective (Noble, 2006). These principles will be illustrated with examples of recent physiological modelling.