Appears in collection : Les probabilités de demain 2017

We begin this expository talk with a discussion of the combinatorics of the nearest-neighbor Ising model in 2D - an archetypical example of a statistical physics system that admits an order-disorder phase transition - and the underlying fermionic structure, which makes it accessible for the rigorous mathematical analysis. We then survey recent results on convergence of correlation functions at the critical temperature to conformally covariant scaling limits given by Conformal Field Theory, as well as the convergence of interfaces (domain walls) to the relevant Conformal Loop Ensemble. Is the case closed? Not at all: there are still many things to understand and to prove, especially for the non-critical and/or non-homogeneous model.