This paper presents a synthesis of the emerging literature related to the trio climate-finance-growth. It sheds light on the pros and cons of the integrated economy-climate models for the analysis of this trio. We first show how in the integrated assessment models, starting with the seminal Nordhaus’ DICE (2014), growth (improperly) takes precedence over the climate-related damages because investments in a low carbon sector systematically crowd-out the others sectors, with detrimental effects on both short term and long term growth. Moreover, in this perfect financial market framework, this re-allocation of resources drags no disturbing consequences. Finally the rational expectations of a representative agent completely determine the economic long-run equilibrium, leaving no place for any lasting financial or monetary effect. We then progressively relax theses hypotheses to put forward a synthesis of the very recent literature, mainly based on neo-keynesian models. Nonetheless, it appears that the integration finance-climate-growth in the economy-climate models is far from being solved.