Phase transitions in the continuum: results and open problems

There are only a few models of particle systems in Rd where a rigorous proof of phase transition is availalble. I will briefly describe the models, sketch the proofs and then focus on the approach proposed by Kac. Its implementation leads to an extension of the Pirogov Sinai theory to perturbations of mean field where techniques of probability theory are complemented with techniques of variational problems and control theory. I will then conclude with some open problems.