Bayesian optimisation is a powerful method for optimising black-box functions, popular in settings where the true function is expensive to evaluate and no gradient information is available. Bayesian optimisation can improve responses to many optimisation problems within climate change for which simulator models are unavailable or expensive to sample from. While there have been several demonstrations of climate-related applications, there has been no unifying review of applications and benchmarks. We provide such a review here, to encourage the use of Bayesian optimisation for important and well-suited applications. We identify four main application domains: material discovery, wind farm layout, optimal renewable control and environmental monitoring. For each domain we identify a public benchmark or data set that is easy to use and evaluate systems against, while being representative of real-world problems. Due to the lack of a suitable benchmark for environmental monitoring, we propose LAQN-BO, based on air pollution data. Our contributions are: a) summarising Bayesian optimisation applications related to climate change; b) identifying a representative range of benchmarks, providing example code where necessary; and c) introducing a new benchmark, LAQN-BO.