Modelling the economics of climate change is daunting. Many existing methodologies from social and physical sciences need to be deployed, and new modelling techniques and ideas still need to be developed. Existing bread-and-butter micro- and macroeconomic tools, such as the expected utility framework, market equilibrium concepts and representative agent assumptions, are far from adequate. Four key issues—along with several others—remain inadequately addressed by economic models of climate change, namely: (1) uncertainty, (2) aggregation, heterogeneity and distributional implications (3) technological change, and most of all, (4) realistic damage functions for the economic impact of the physical consequences of climate change. This paper assesses the main shortcomings of two generations of climate-energy-economic models and proposes that a new wave of models need to be developed to tackle these four challenges. This paper then examines two potential candidate approaches—dynamic stochastic general equilibrium (DSGE) models and agent-based models (ABM). The successful use of agent-based models in other areas, such as in modelling the financial system, housing markets and technological progress suggests its potential applicability to better modelling the economics of climate change.