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In this position paper on reliable networks, we discuss new trends in the design of reliable communication systems. We focus on a wide range of research directions including protection against software failures as well as failures of communication systems equipment. In particular, we outline future research trends in software failure mitigation, reliability of wireless communications, robust optimization and network design, multilevel and multirealm network resilience, multiple criteria routing approaches in multilayer networks, resilience options of the fixed IP backbone network in the interplay with the optical layer survivability, reliability of cloud computing networks, and resiliency of software-defined networks. Described research directions are frequently enhanced with examples.