Segregation problems arise when competing species tend to occupy disjoint regions, leading naturally to a free boundary separating them. In this talk, we will discuss a parabolic model in which the diffusion is governed by fully nonlinear operators. We will describe the main ideas behind the existence of Lipschitz solutions, the free boundary condition, and the regularity of the interface near nondegenerate points. This is ongoing joint work with Emily Casey (U. Minnesota), Cornelia Mihaila (Saint Michael’s College), and Clara Torres-Latorre (ICMAT).