Complex climate models that describe the evolution of the coupled ocean atmosphere cryosphere system are gradually extended to “non physical” components of the earth system, and account for land vegetation dynamics, ocean biology, global biogeochemistry and atmospheric chemistry. In the future, these models will have to better represent the potential feedbacks with society and therefore to couple the natural bio-physical components with the socio-economic system. The paper will review the present status of complex climate and Earth system models, report some preliminary attempts to include societal aspects, and highlight challenges for future research.