Information and communication technologies are increasingly pervasive in our everyday lives. Their use has greatly evolved from an ancillary service to a component of all our activities, anytime, anywhere. To this aim, we rely heavily on cloud computing and, more recently, on edge computing. Hence, their contribution (or obstruction) to the sustainability of our society at large is pivotal. Unfortunately, cloud/edge provisioning has a dark side: it too often prioritizes economic gain over the cost of long-lasting sustainability. Also, sustainability is often absent from the discussions in the cloud/edge research community. To start the discussion and highlight a number of sustainability shortcomings of the cloud and edge computing paradigms, we carry out an exploratory study involving experts-in-the-field, capture their inputs in the form of so-called unsustainable patterns, and complement them with examples of possible countermeasures. The results of our study include: (i) the definition of a Pattern Model, (ii) a catalog of unsustainable patterns for the cloud and edge computing paradigms, and (iii) the identification of preliminary countermeasures and takeaways in order to make these two paradigms more sustainable.