In some cases, it is possible to find, analytically, the stationary solution of the master equation. The problem of classical diffusion in complex networks is to understand how a quantity will flow through the system and how much time it will take to reach the stationary state. Classical diffusion in multiplex networks has been recently studied by introducing the concept of supra-adjacency matrix, later recognized as a special flattening of the multilayer adjacency tensor. In tensorial notation, the diffusion equation on the top of a general multilayer system can be written, concisely, as  formula_129  where formula_130 is the amount of diffusing quantity at time formula_70 in node formula_27 in layer formula_31. The rank-4 tensor governing the equation is the Laplacian tensor, generalizing the combinatorial Laplacian matrix of unidimensional networks. It is worth remarking that in non-tensorial notation, the equation takes a more complicated form. Many of the properties of this diffusion process are completely understood in terms of the second smallest eigenvalue of the Laplacian tensor. It is interesting that diffusion in a multiplex system can be faster than diffusion in each layer separately, or in their aggregation, provided that certain spectral properties are satisfied. Recently, how information (or diseases) spread through a multilayer system has been the subject of intense research. Buldyrev et al. developed a framework to study percolation in multilayer networks with dependency links between the layers. New physical phenomena has been found, including abrupt transitions and cascading failures. When the networks are embedded in space they become extremely vulnerable even for a very small fraction of dependency links and for localized attacks on a zero fraction of nodes. When recovery of nodes is introduced, a rich phase diagram is found that include multicritical points, hysteresis and metastable regimes. A dynamic dependency approach representing interdependence of dynamic systems, such as synchronization and spreading has been developed based on multilayer networks. The study found phenomena such as coupled collective phenomena, including multistability, hysteresis, regions of coexistence, and macroscopic chaos.