Most natural and engineered systems include multiple subsystems that are organized as layers of connectivity. It is important to take such features into account to try to improve our understanding of these complex systems. It is thus necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion and the physical properties that emerge in this new setup. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. Multilayered interconnected networks, and in particular what has been calledmultiplex networks, explicitly incorporate multiple (and independent) channels of connectivity in a system. They provide a natural description for systems in which entities have a different set of neighbors in each layer (which can represent, e.g., a task, an activity, or a category). A fundamental aspect of describing multiplex networks is defining and quantifying the interconnectivity between different categories of connections. This amounts to switching between layers in a multilayer system, and the associated interlayer connections in a network are responsible for the emergence of new phenomena in multiplex networks. Interlayer connections can generate new structural and dynamical correlations between components of a system, so it is important to develop a framework that takes them into account. The study of these systems is of utmost importance to understand more realistic structured interactions.