  The science of networks has revolutionised research into the dynamics of
interacting elements. It could be argued that epidemiology in particular has
embraced the potential of network theory more than any other discipline. Here
we review the growing body of research concerning the spread of infectious
diseases on networks, focusing on the interplay between network theory and
epidemiology. The review is split into four main sections, which examine: the
types of network relevant to epidemiology; the multitude of ways these networks
can be characterised; the statistical methods that can be applied to infer the
epidemiological parameters on a realised network; and finally simulation and
analytical methods to determine epidemic dynamics on a given network. Given the
breadth of areas covered and the ever-expanding number of publications, a
comprehensive review of all work is impossible. Instead, we provide a
personalised overview into the areas of network epidemiology that have seen the
greatest progress in recent years or have the greatest potential to provide
novel insights. As such, considerable importance is placed on analytical
approaches and statistical methods which are both rapidly expanding fields.
Throughout this review we restrict our attention to epidemiological issues.
