For various reasons, the cloud computing paradigm is unable to meet certain requirements (e.g. low latency and jitter, context awareness, mobility support) that are crucial for several applications (e.g. vehicular networks, augmented reality). To fulfil these requirements, various paradigms, such as fog computing, mobile edge computing, and mobile cloud computing, have emerged in recent years. While these edge paradigms share several features, most of the existing research is compartmentalised; no synergies have been explored. This is especially true in the field of security, where most analyses focus only on one edge paradigm, while ignoring the others. The main goal of this study is to holistically analyse the security threats, challenges, and mechanisms inherent in all edge paradigms, while highlighting potential synergies and venues of collaboration. In our results, we will show that all edge paradigms should consider the advances in other paradigms.