Soon after the celebrated solution of the two-dimensional
Ising model several researchers addressed the issue of the stability of
the emerging (qualitative and quantitative) picture in presence of
'impurities'. It was first believed that transitions cannot survive to
quenched disorder (a more technical language for impurities), but later
it became clear that certain transitions do persist and the work of A.
B. Harris (1974) introduced very influential ideas on this issue. The
aim of the talk is to present Harris' approach in its original context
(Ising model) and some of what has been done on and around it, in the
light of the recent rigorous results obtained for disordered pinning
models.


[Invited by Ch. Mazza]