ABSTRACT The financial sector, by mobilizing capital, is fundamental to adapt and mitigate the impact of climate change in the economy. This has led to the emergence of a new research field, climate finance, where experts are starting to harness Machine Learning (ML) as a tool to solve new problems, due to the need to use big datasets and to model complex non-linear relationships. We propose a review of the academic literature that goes beyond the existing bibliometric studies in the field, with the aim of identifying relevant application domains of this technology to inform ML experts where and how their modeling expertise may add value in climate finance. To achieve this, we first assemble a corpus of texts from three scientific databases and use Latent Dirichlet Allocation (LDA) for topic modeling, to uncover seven research areas which we label as: natural hazards, biodiversity, agricultural risk, carbon markets, energy economics, Environmental, Social and Governance (ESG) factors & investing, and climate data. Second, we perform an analysis of publication trends, which confirms that ML is growing both in breadth and depth in climate finance, in particular topics related to energy economics, ESG factors and climate data. Interestingly, some methods stand out in each area, based on data characteristics and modeling requirements.