A wide range of communicable human diseases can be considered as spreading through a network of possible transmission routes. The implied network structure is vital in determining disease dynamics, especially when the average number of connections per individual is small as is the case for many sexually transmitted diseases (STDs). Here we develop an intuitive mathematical framework to deal with the heterogeneities implicit within contact networks and those that arise because of the infection process. These models are compared with full stochastic simulations and show excellent agreement across a wide range of parameters. We show how such models can be used to estimate parameters of epidemiological importance, and how they can be extended to examine the effectiveness of various control strategies, in particular screening programs and contact tracing.