This chapter raises key questions on the current state of practice in policy appraisal and analysis, in academia and government. It proposes a fundamental methodological shift in the modelling of policy interventions for sustainability transitions in order to account for complexity, uncertainty and agent heterogeneity. It identifies the main shortcomings of present methods of the equilibrium and optimisation-based approaches most frequently used to inform sustainability policy: (i) their normative, optimisation-based nature, (ii) their unrealistic reliance on the full-rationality of agents, (iii) their inability to capture self-reinforcing feedback processes, (iv) their inability to represent multiple solutions and path-dependency, and (v) their inability to properly account for agent heterogeneity. A proposal is made for dynamical systems analysis in policy appraisal that could lead to a paradigm shift in the ability of governments to understand and solve complex environmental issues.