This paper debates on notions of context-awareness as a relevant asset of networking and computing architectures for an Internet of Things (IoT), in particular in regards to a smoother support of the the networking operation between Cloud and Edge. Specifically, the paper debates on notions of contextawareness and goes over different types of context-awareness indicators that are being applied to Edge selection algorithms, covering the approaches currently used, the role of the algorithms applied, their scope, and contemplated performance metrics. Lastly, the paper provides guidelines for future research in the context of Cloud-Edge and the application of context-awareness to assist in a higher degree of automation of the network and, as consequence, a better support of the Cloud to Edge continuum. INDEX TERMS Context-awareness, Internet of Things (IoT), Edge/Fog Computing.