Multilayer networks are a new paradigm in the study of complex interconnected systems, as they allow to cast into a single framework the complex topological and dynamical interdependencies between different networked systems. In this talk, we first provide a brief overview of what is the state-of-the-art in network science, paying special attention to multilayer networks. Then, in order to discuss some specific case studies, we present results concerning how to characterize diffusion processes that take place on top of these systems as well as on what new insights can be gained using multilayer approaches to study interdependent transportation systems.