Cellular networks represent a critical infrastructure and their security is thus crucial. 5G - the latest generation of cellular networks - combines different technologies to increase capacity, reduce latency, and save energy. Due to its complexity and scale, however, ensuring its security is extremely challenging. In this white paper, we outline recent approaches supporting systematic analyses of 4G LTE and 5G protocols and their related defenses and introduce an initial security and privacy roadmap, covering different research challenges, including formal and comprehensive analyses of cellular protocols as defined by the standardization groups, verification of the software implementing the protocols, the design of robust defenses, and application and device security.