Isoradial graphs are a natural generalization of regular graphs which give,
for many models of statistical mechanics, the right framework for studying
models at criticality. In this survey paper, we first explain how isoradial
graphs naturally arise in two approaches used by physicists: transfer matrices
and conformal field theory. This leads us to the fact that isoradial graphs
provide a natural setting for discrete complex analysis, to which we dedicate
one section. Then, we give an overview of explicit results obtained for
different models of statistical mechanics defined on such graphs: the critical
dimer model when the underlying graph is bipartite, the 2-dimensional critical
Ising model, random walk and spanning trees and the q-state Potts model.Comment: 22 page
