Network communications and the Internet pervade our daily activities so deeply that we strongly depend on the availability and quality of the services they provide. For this reason, natural and technological disasters, by affecting network and service availability, have a potentially huge impact on our daily lives. Ensuring adequate levels of resiliency is hence a key issue that future network paradigms, such as 5G, need to address. This paper provides an overview of the main avenues of research on this topic within the context of the RECODIS COST Action.