Edge computing has emerged as a distributed computing paradigm to overcome practical scalability limits of cloud computing. The main principle of edge computing is to leverage on computational resources outside of the cloud for performing computations closer to data sources, avoiding unnecessary data transfers to the cloud and enabling faster responses for clients. While this paradigm has been successfully employed to improve response times in some contexts, mostly by having clients perform pre-processing and/or filtering of data, or by leveraging on distributed caching infrastructures, we argue that the combination of edge and cloud computing has the potential to enable novel applications. However, to do so, some significant research challenges have to be tackled by the computer science community. In this paper, we discuss different edge resources and their potential use, motivated by envisioned use cases. We then discuss concrete research challenges that are in the critical path towards realizing our edge vision. We conclude by proposing a research agenda to allow the full exploitation of the potential for the emerging hybrid cloud/edge paradigm.