The vision of this proposal is to advance our understanding of the interplay between combinatorics and probability theory. The intersection between these fields has gained increasing attention in the past decades. Important topics include, for example, the study of random discrete structures and associated stochastic processes as well as the analysis of algorithms. There are also connections to statistical physics, theoretical computer science, and mathematical biology. Our focus is on the mathematical study of probabilistic models exhibiting condensation phenomena, in particular branching processes, random planar graphs, and Gibbs partitions.