Heterogeneous and multilayer networks are networks where different protocols coexist and where encapsulations take place. These networks are becoming more widespread (IPv4/IPv6 coexistence, VPN networks, IoT networks, etc.). More generally, any network allowing the establishment of tunnels can be considered as an heterogeneous or multilayer network. Today, tunnels are ubiquitous in networks. However, the models and the algorithms that can be applied on them are not adapted to take tunnels into account. It turns out that simple problems in a conventional network, such as path computation and routing, become very difficult in a multilayer network (the computation of a path under bandwidth constraint is trivially polynomial in a conventional network, but is NP-hard in a multilayer network. Similarly, the length of a path in such a network can be exponential). These problems are not well understood and it is necessary to develop new models and new algorithms to solve them. The aim of this thesis is to study the communication problems in such networks, in particular the centralized and distributed path computation, the multicast communication via the computation of diffusion trees, as well as the adaptation of these algorithms in routing protocols. This thesis is part of the ANR project JCJC HEterogeneity and Routing Algorithms in networks (HERA), whose goal is to better understand the theoretical structural and algorithmic foundations of multilayer networks. Thesis manuscript is accessible here: https://www.labri.fr/perso/nmouhoub/pdf/phd_thesis.pdf