This chapter presents a visual process calculus for designing and simulating computer models of biological systems. The calculus is based on a graphical variant of stochastic pi-calculus extended with mobile compartments, and the simulation algorithm is based on standard kinetic theory of physical chemistry. The calculus forms the basis of a formal visual programming language for biology. The basic primitives of the calculus are first introduced by a series of examples involving genes and proteins. More complex features of the calculus are then illustrated by examples involving gene networks, cell differentiation, and immune system response. The main benefit of the calculus is its ability to model large systems incrementally, by directly composing simpler models of subsystems. The formal nature of the calculus also facilitates mathematical analysis of models, which in future could help provide insight into some of the underlying properties of biological systems.