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Abstract Climate changepoint (homogenization) methods abound today, with a myriad of techniques existing in both the climate and statistics literature. Unfortunately, the appropriate changepoint technique to use remains unclear to many. Further complicating issues, changepoint conclusions are not robust to perturbations in assumptions; for example, allowing for a trend or correlation in the series can drastically change changepoint conclusions. This paper is a review of the topic, with an emphasis on illuminating the models and techniques that allow the scientist to make reliable conclusions. Pitfalls to avoid are demonstrated via actual applications. The discourse begins by narrating the salient statistical features of most climate time series. Thereafter, single- and multiple-changepoint problems are considered. Several pitfalls are discussed en route and good practices are recommended. While most of our applications involve temperatures, a sea ice series is also considered. Significance StatementThis paper reviews the methods used to identify and analyze the changepoints in climate data, with a focus on helping scientists make reliable conclusions. The paper discusses common mistakes and pitfalls to avoid in changepoint analysis and provides recommendations for best practices. The paper also provides examples of how these methods have been applied to temperature and sea ice data. The main goal of the paper is to provide guidance on how to effectively identify the changepoints in climate time series and homogenize the series.