•Distributional effects of carbon tax within both household and economic sectors are examined.•The effects of ex-ante and ex-post preferential measures are categorized and compared.•We analyze the progress and shortcomings of existing studies.•We put forward implications for policy-making and future research. The carbon tax is a frequently discussed economic instrument for carbon emissions mitigation and prevention of global climate change. However, a range of issues may emerge when introducing a carbon tax; among these issues, the distributional impact has been frequently highlighted as an obstacle to the public acceptance of such a mitigation policy. This literature review focuses specifically on the distributional effects of carbon taxes and contributes to existing studies by providing a classification and discussion on how to comprehensively assess distributional impacts and what measures can be taken to mitigate the potential adverse distributional impact. We confirm that a pure carbon tax without revenue recycling in developed economies tends to be regressive, i.e. lower income households being more affected, while our research does not support the perception that it reveals progressivity in developing countries. In terms of its effects on economic sectors, we find that sectors with higher energy intensity are more affected by a uniform carbon tax, while preferential measures to protect these industries face a trade-off between environmental effectiveness and economic growth. We also stress that different designs for carbon tax mechanisms play a key role in affecting the distributional impacts and impacts in other policy arenas, indicating that trade-offs between efficiency and equity always exist when designing a carbon tax. This study may help to identify the shortcomings of existing designs and puts forward practical implications for future research; moreover, it offers valuable information to help policy-makers to understand the trade-off between equity and efficiency when designing a carbon tax.