The overall objective of this paper is to scrutinize previous economic models used to assess the economic costs of climate policy. We pay particular attention to the way in which different model structures and assumptions affect cost estimates, and highlight the limitations and the strengths of different types of modelling approaches. The paper begins by briefly discussing the concept of economic costs, different cost categories (i.e., direct costs, partial equilibrium costs and general equilibrium costs), and the various model approaches that can be used to assess the economic impacts of climate policy (e.g., top-down versus bottom-up models). A systematic review of the main assumptions and methodological choices that underlie different reported cost estimates is presented, and we distinguish between five main types of climate policy cost drivers: a) the baseline scenario; b) the structural characteristics of the models; c) the representation of technological change (e.g., endogenous or exogenous); d) the design of climate policy; and e) the inclusion of non-market costs and benefits. The analysis shows that all these elements help explain model outcomes.