The concept of Cognitive Radio (CR) has emerged as a practical solution to solve the issue of the fixed spectrum and bandwidth scarcity in wireless communication. However, the nature of dynamic Mobile Cognitive Radio Networks (MCRNs) drives to the emergence of new challenges, especially concerning the routing protocol operations. Applying a cross-layer design is considered a sufficient remedy to overcome routing protocol challenges such (e.g. channel diversity, integration route discovery with spectrum decision, mobility, etc.). Consequently, the cross-layer design has a magic solution to overwhelm routing challenges in MCRNs due to the ability to be free from the strict boundary and share the information and services with other layers in a manner that contributes to enhancing routing performance. Thus, the scope of this survey is to review and taxonomy numerous routing protocols in MCRNs according to methods of design to highlight the strength and weakness points. Also, machine learning has acquired much interest in this literature. A cross-layer framework for smart routing protocol in MCRNs has been proposed by exploiting machine learning mechanisms. Finally, the open research issues of routing protocol in MCRNs are summed up.INDEX TERMS Mobile cognitive radio network, cross-layer design, non-cross-layer design, machine learning, smart routing protocol.