Decisions about climate change are inherently moral. They require making moral judgements about important values and the desired state of the present and future world. Hence there are potential benefits in explaining climate action by integrating well-established and emerging knowledge on the role of morality in decision-making. Insights from the social and behavioural sciences can help ground climate change decisions in empirical understandings of how moral values and worldviews manifest in people and societies. Here, we provide an overview of progress in research on morals in the behavioural and social sciences, with an emphasis on empirical research. We highlight the role morals play in motivating and framing climate decisions; outline work describing morals as relational, situated, and dynamic; and review how uneven power dynamics between people and groups with multiple moralities shape climate decision-making. Effective and fair climate decisions require practical understandings of how morality manifests to shape decisions and action. To this end, we aim to better connect insights from social and behavioural scholarship on morality with real-world climate change decision-making.