<p>In the Allen–Cahn theory of phase transitions, minimizers partition the domain in subregions, the sets where a minimizer is near to one or to another of the zeros of the potential. These subregions that model the phases are separated by a tiny <i>Diffuse Interface</i>. Understanding the shape of this diffuse interface is an important step toward the description of the structure of minimizers. We assume Dirichlet data and present general conditions on the domain and on the boundary datum ensuring the connectivity of the diffuse interface. Then we restrict to the case of two dimensions and show that the phases can be separated, in a certain optimal way, by a connected <i>network</i> with a well-defined structure. This network is contained in the diffuse interface and is a priori unknown. Under general assumption on the potential and on the Dirichlet datum, we show that, if we assume the connectivity of the phases, then we can obtain precise information on the shape of the network and in turn a detailed description of the fine structure of minimizers. In particular, we can characterize the shape and the size of the various phases and also how they depend on the surface tensions. These results were announced at the 8th IST-IME Meeting in September 2022 in Lisbon.</p>