Numerous weather and climate extremes have broken long-standing observed records. These record-breaking (or record-shattering if the margin is large) events have substantial socioeconomic impacts and pose adaptation and planning challenges. In this Review, we assess observed and projected changes in record-breaking climate extremes. Record occurrence can be understood with statistical considerations, and their changes quantified as the record ratio — the observed frequency of record events relative to a stationary climate. Many climate variables have witnessed changes in their record-breaking frequency. For example, all-time daily hot records on land are more than four times higher in 2016–2024 than expected without climate change, and all-time cold records two times lower; similarly, daily maximum precipitation records and monthly dryness records are more than 40% and 10% higher, respectively. In the future, slowing the rate of warming reduces record ratios, highlighting the benefits of mitigation. For instance, by the end of the century, multimodel mean record hot events are projected to be 15.7 more likely than in a stationary climate under SSP3-7.0, but only ~2.9 and ~1.8 more likely for SSP1-2.6 and SSP1-1.9, respectively, lower than those observed today. New record cold will become virtually non-existent under all emission scenarios. Among others, records have also been broken for ice loss, sea ice and ocean heat content, but quantifying record statistics is challenged by data availability, duration and quality. Addressing these data challenges and developing statistical methods to account for multivariate records are research priorities.