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Cognitive radio networks (CRNs) are composed of cognitive, spectrum-agile devices capable of changing their configurations on the fly based on the spectral environment. This capability opens up the possibility of designing flexible and dynamic spectrum access strategies with the purpose of opportunistically reusing portions of the spectrum temporarily vacated by licensed primary users. On the other hand, the flexibility in the spectrum access phase comes with an increased complexity in the design of communication protocols at different layers. This work focuses on the problem of designing effective routing solutions for multi-hop CRNs, which is a focal issue to fully unleash the potentials of the cognitive networking paradigm. We provide an extensive overview of the research in the field of routing for CRNs, clearly differentiating two main categories: approaches based on a full spectrum knowledge, and …