Much of the work on climate change and its economic impacts so far has been done on the basis of equilibrium theories, in the climate as well as the economic realm. Increasingly, though, the climate sciences community has come to realize that natural climate variability is an important issue in assessing climate evolution on time scales of years-to-decades. Somewhat less broad and consensual is the incipient use of nonequilibrium, stochastic-dynamic models in the macroeconomic literature. The purpose of this chapter is to cover some of the advances in the recent climate and economic literature on the use of such models to address climate change mitigation and adaptation. The chapter stresses the importance of taking into account the nonlinearities in both the climate and economic system, as well as in the coupling. Some of these issues are illustrated by reviewing work on a coupled climate–economy–biosphere (CoCEB) model with random shocks, designated as CoCEB-S. This review emphasizes the latter model’s results on the comparative efficacy of approaches to abatement – such as low-carbon technology, deforestation reduction, or carbon capture and storage – and it uses the evolution of the inclusive wealth index as its key policy evaluation tool.