  Critical behavior at an order/disorder phase transition has been a central
object of interest in statistical physics. In the past century, techniques
borrowed from many different fields of mathematics (Algebra, Combinatorics,
Probability, Complex Analysis, Spectral Theory, etc) have contributed to a more
and more elaborate description of the possible critical behaviors for a large
variety of models. The Ising model is maybe one of the most striking success of
this cross-fertilization, for this model of ferromagnetism is now very well
understood both physically and mathematically. In this article, we review an
approach, initiated in \cite{GriHurShe70,Aiz82} and based on the notion of
random currents, enabling a deep study of the model.
