Cognitive radio networks are smart networks that automatically sense the channel and adjust the network parameters accordingly. Cognitive radio is an emerging technology that enables the dynamic deployment of highly adaptive radios that are built upon software defined radio technology. The radio technology allows the unlicensed operation to be in the licensed band. The cognitive radio network paradigm therefore raises many technical challenges that appear in different layers, such as the power efficiency, spectrum management, spectrum detection, environment awareness, and distributed spectrum measurements in the physical layer, the route selection as well as the route robustness in the network layer, and the security issues like the unauthorized intrusion and malicious users in the application layer. In this paper we aim at presenting an overview of research issues especially in network and application layers as well as the proposed solutions for them.