Coarse-graining techniques for (random) Kac models

We review our recent results on the low temperature behavior of Kac models. We discuss translation-invariant models and the Kac version of the random field model. For the latter we outline, how various coarse-graining techniques can be used to prove ferromagnetic ordering in dimensions $d\geq 3$, small randomness, and low temperatures, uniformly in the range of the interaction