As climate change progresses, the risk of adverse impacts on vulnerable populations is growing. As governments seek increased and drastic action, policymakers are likely to seek quantification of climate-change impacts and the consequences of mitigation policies on these populations. Current models used in climate research have a limited ability to represent the poor and vulnerable, or the different dimensions along which they face these risks. Best practices need to be adopted more widely, and new model features that incorporate social heterogeneity and different policy mechanisms need to be developed. Increased collaboration between modellers, economists, and other social scientists could aid these developments. We review the history and state of the art of models used in climate research, including integrated assessment models (IAMs) and national studies, and those that model mitigation and climate-change impacts. We assess how and to what extent they represent distributional impacts within countries. We argue that there is much scope to improve the representation of income distribution and poverty. Given the diversity of models, this endeavour presents fundamental challenges for some models, but possibly requires only incremental changes in others.