Abstract-The cognitive radio is an emerging technology that enables dynamic spectrum access in wireless networks. The cognitive radio is capable of opportunistically using the available portions of a licensed spectrum to improve the application performance for unlicensed users. The opportunistic use of the available channels in the wireless environment requires dynamic channel assignment to efficiently utilize the available resources while minimizing the interference in the network. A challenging aspect of such algorithms is the incorporation of the channels' diverse characteristics, highly dynamic network conditions with respect to primary users' activity, and different fragmented sizes of the available channels. This paper presents a comprehensive survey on the state-of-the-art channel assignment algorithms in cognitive radio networks. We also classify the algorithms by presenting a thematic taxonomy of the current channel assignment algorithms in cognitive radio networks. Moreover, the critical aspects of the current channel assignment algorithms in cognitive radio networks are analyzed to determine the strengths and weaknesses of such algorithms. The similarities and differences of the algorithms based on the important parameters, such as routing dependencies, channel models, assignment methods, execution model, and optimization objectives, are also investigated. We also discuss open research issues and challenges of channel assignment in the cognitive radio networks.