The cognitive radio (CR) paradigm for designing next‐generation wireless communications systems is becoming increasingly popular, and different aspects of it are being implemented in currently available wireless systems. In the last decade, a significant amount of research efforts has been made to solve CR challenges, and several standards related to CR and dynamic spectrum access have been developed. Also, there have been advances in software‐defined radio platforms to implement the CR systems. In this article, we provide a comprehensive survey on the evolution of CR research covering aspects such as spectrum sensing, measurements and statistical modeling of spectrum usage, physical layer aspects such as waveform and modulation design, multiple access, resource allocation and power control, cognitive learning, adaptation and self‐configuration, multihop transmission and routing, and robustness and security in CR networks. Also, state‐of‐the‐art research on the economics of CR networks, CR simulation tools, testbeds and hardware prototypes, CR applications, and CR standardization efforts is summarized. Emerging trends on CR research and open research challenges related to the cost‐effective and large‐scale deployment of CR systems are outlined. Copyright © 2013 John Wiley & Sons, Ltd.