Cognitive radio networks (CRN), in their quest to become the preferred next-generation wireless communication paradigm, will depend heavily on their ability to efficiently manage the limited resources at their disposal in meeting the demands of their numerous users and driving their operations. As a result, a considerable amount of research work has been recently dedicated to investigating and developing resource allocation (RA) models that capture the essentials of CRN. The various ideas put forward by researchers to address RA problems in CRN have been somewhat diverse, and somehow, there seem to be no links that bring cohesion and clarity of purpose and ideas. To address this problem and bridge the gap, in this paper, a comprehensive study on the prevalent techniques developed for addressing RA problems in CRN is carried out, with an intent to put some structure, relevance and meaning to the various solution approaches. The solution models are therefore grouped and/or classified based on certain outstanding criteria, and their strengths and weaknesses highlighted. Open-ended problems are identified, and suggestions for improving solution models are given. The study therefore gives good directions for further investigations on developing RA solutions in CRN.