Cognitive radio networks (CRNs) have emerged as an essential technology to enable dynamic and opportunistic spectrum access which aims to exploit underutilized licensed channels to solve the spectrum scarcity problem. Despite the great benefits that CRNs offer in terms of their ability to improve spectrum utilization efficiency, they suffer from user location privacy issues. Knowing that their whereabouts may be exposed can discourage users from joining and participating in the CRNs, thereby potentially hindering the adoption and deployment of this technology in future generation networks. The location information leakage issue in the CRN context has recently started to gain attention from the research community due to its importance, and several research efforts have been made to tackle it. However, to the best of our knowledge, none of these works have tried to identify the vulnerabilities that are behind this issue or discuss the approaches that could be deployed to prevent it. In this paper, we try to fill this gap by providing a comprehensive survey that investigates the various location privacy risks and threats that may arise from the different components of this CRN technology, and explores the different privacy attacks and countermeasure solutions that have been proposed in the literature to cope with this location privacy issue. We also discuss some open research problems, related to this issue, that need to be overcome by the research community to take advantage of the benefits of this key CRN technology without having to sacrifice the users' privacy.