Hybrid societies are self-organizing, collective systems, which are composed of different components, for example, natural and artificial parts (bio-hybrid) or human beings interacting with and through technical systems (socio-technical). Many different disciplines investigate methods and systems closely related to the design of hybrid societies. A stronger collaboration between these disciplines could allow for re-use of methods and create significant synergies. We identify three main areas of challenges in the design of self-organizing hybrid societies. First, we identify the formalization challenge. There is an urgent need for a generic model that allows a description and comparison of collective hybrid societies. Second, we identify the system design challenge. Starting from the formal specification of the system, we need to develop an integrated design process. Third, we identify the challenge of interdisciplinarity. Current research on self-organizing hybrid societies stretches over many different fields and hence requires the re-use and synthesis of methods at intersections between disciplines. We then conclude by presenting our perspective for future approaches with high potential in this area.