Language models (LMs) have attracted the attention of researchers from the natural language processing (NLP) and machine learning (ML) communities working in specialized domains, including climate change. NLP and ML practitioners have been making efforts to reap the benefits of LMs of various sizes, including large language models, in order to both simplify and accelerate the processing of large collections of text data, and in doing so, help climate change stakeholders to gain a better understanding of past and current climate-related developments, thereby staying on top of both ongoing changes and increasing amounts of data. This paper presents a brief history of language models and ties LMs’ beginnings to them becoming an emerging technology for analysing and interacting with texts in the specialized domain of climate change. The paper reviews existing domain-specific LMs and systems based on general-purpose large language models for analysing climate change data, with special attention being paid to the LMs’ and LM-based systems’ functionalities, intended use and audience, architecture, the data used in their development, the applied evaluation methods, and their accessibility. The paper concludes with a brief overview of potential avenues for future research vis-à-vis the advantages and disadvantages of deploying LMs and LM-based solutions in a high-stakes scenario such as climate change research. For the convenience of readers, explanations of specialized terms used in NLP and ML are provided.