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This paper provides a comprehensive overview of the modelling tools available for integrating climate change impacts into pest risk assessments (PRA), elucidating the existing methodologies and models employed to understand the potential distributions of pests based on historical data and under future climate change scenarios. We highlight the strengths and weaknesses of these models and provide commentary on their ability to identify emerging threats due to climate change accurately and adequately, considering pest establishment likelihood, host crop exposure and the distribution of impacts. The simplest methods are based on climate‐matching models, degree‐day development models and Köppen–Geiger climate classification. Correlative species distribution models derive species–environment relationships and have been applied to PRA with mixed success. When fitted models are applied to different continents they are usually challenged to extrapolate climate suitability patterns outside the climate space used to train them. Global climate change is creating novel climates, exacerbating this 'transferability' problem. Some tools have been developed to reveal when these models are extrapolating. Process‐oriented models, which focus on mechanisms and processes rather than distribution patterns, are inherently more reliable for extrapolation to novel climates such as new continents and future climate scenarios. These models, however, require more skill and generally more knowledge of the species to craft robust models. [ABSTRACT FROM AUTHOR]