Currently there is an active debate about how the existing cloud paradigm can cope with the volume, variety, and velocity of the data generated by end devices (e.g., Internet of Things sensors). It is expected that there will be over 50 billion of these devices by 2020, which will create more than two Exabytes worth of data each day. Additionally, the vast number of edge devices create a huge ocean of digital resources close to the data source, which, however, remain so far unexploited to their full extent. EXEGESIS proposes to harness these unutilized resources via a three-layer architecture that encompasses the mist, fog, and cloud. The mist network is located at the very bottom, where interconnected objects (Internet of Things devices, small servers, etc.) create neighborhoods of objects. This arrangement is enhanced by a virtual fog layer, which allows for dynamic, ad hoc interconnections among the various neighborhoods. At the top layer resides the cloud with its abundant resources that can also be included in one or more virtual fog neighborhoods. Thus, this article complements and leverages existing cloud architectures, enabling them to interact with this new edge-centric ecosystem of devices/resources, and benefit from the fact that critical data are available where they can add the most value.