Implementing an effective climate policy is one of the main challenges for our future. Even though ambitious mitigation targets are necessarily costly, curbing GHG emissions can prevent future irreversible impacts of climate change on human kind and the environment. Climate policy is therefore crucial for present and future generations. Nonetheless, one may wonder whether the economic and social dimensions of future global development could be harmed by climate policy. This paper addresses this question by examining some recent developments in international climate policy and considering different levels of cooperation that may arise in light of the outcomes of the Conference of the Parties recently held in Doha. Then it explores whether the implementation of various climate policy scenarios would help enhancing sustainability or rather whether there is a trade-off between climate policy and economic development and/or social cohesion. This is done by using a new comprehensive indicator, the FEEM Sustainability Index (FEEM SI), which aggregates several economic, social, and environmental indicators. The FEEM SI index is built into a recursive-dynamic Computable General Equilibrium (CGE) model of the world economy, thus offering the possibility of projecting all indicators into the future, and therefore delivering a perspective assessment of sustainability under different future climate policy scenarios. We find that the environmental component of sustainability improves at the regional and world level thanks to the GHG emission reductions achieved through climate policy. However, the economic and social components are affected negatively yet marginally. Hence, overall sustainability increases in all scenarios. If the USA, Canada, Japan and Russia would not contribute to mitigating future GHG emissions, as envisioned in one of our scenarios, sustainability in these countries would decrease and the overall effectiveness of climate policy in enhancing global sustainability would be offset.