5G networks will use novel technological concepts to meet the requirements of broadband access everywhere, high user and device mobility, and connectivity of massive number of devices (e.g., the Internet of Things) in an ultra-reliable and affordable way. Software defined networking and network functions virtualization leveraging the advances in cloud computing such as mobile edge computing are the most sought out technologies to meet these requirements. However, securely using these technologies and providing user privacy in future wireless networks are the new concerns. Therefore, this article provides an overview of the security challenges in clouds, software defined networking, and network functions virtualization, and the challenges of user privacy. Henceforth, this article presents solutions to these challenges and future directions for secure 5G systems.