Appears in collection : 100 (102!) Years of the Ising Model

I will review old and present new results on standard and long-range Ising models in dimension 1, 2 and 3. I shall focus on fluctuations or rigidity of interfaces at low temperature, in the coexistence regime.

Based on works in collaboration with Y. Velenik (Geneva) on one hand, and A. van Enter (Groningen), A. Le Ny (Paris) and W. Ruszel (Utrecht) on the other hand, ongoing works with R. Durand (Grenoble).