Vehicular Edge Computing (VEC), based on the Edge Computing motivation and fundamentals, is a promising technology supporting Intelligent Transport Systems services, smart city applications, and urban computing. VEC can provide and manage computational resources closer to vehicles and end-users, providing access to services at lower latency and meeting the minimum execution requirements for each service type. This survey describes VEC’s concepts and technologies; we also present an overview of existing VEC architectures, discussing them and exemplifying them through layered designs. Besides, we describe the underlying vehicular communication in supporting resource allocation mechanisms. With the intent to overview the risks, breaches, and measures in VEC, we review related security approaches and methods. Finally, we conclude this survey work with an overview and study of VEC’s main challenges. Unlike other surveys in which they are focused on content caching and data offloading, this work proposes a taxonomy based on the architectures in which VEC serves as the central element. VEC supports such architectures in capturing and disseminating data and resources to offer services aimed at a smart city through their aggregation and the allocation in a secure manner.