The widespread use of mobile devices, as well as the increasing popularity of mobile services has raised serious cybersecurity challenges. In the last years, the number of cyberattacks has grown dramatically, as well as their complexity. Traditional cybersecurity systems have failed to detect complex attacks, unknown malware, and they do not guarantee the preservation of user privacy. Consequently, cybersecurity systems have embraced Deep Learning (DL) models as they provide efficient detection of novel attacks and better accuracy. This paper presents a comprehensive survey of recent cybersecurity works that use DL in mobile and wireless networks. It covers all cybersecurity aspects: infrastructure threads and attacks, software attacks and privacy preservation. First, we provide a detailed overview of DL techniques applied, or with potential applications, to cybersecurity. Then, we review cybersecurity works based on DL. For each cybersecurity threat or attack, we discuss the challenges for using DL methods. For each contribution, we review the implementation details and the performance of the solution. In a nutshell, this paper constitutes the first survey that provides a complete review of the DL methods for cybersecurity. Given the analysis performed, we identify the most effective DL methods for the different threats and attacks.