Global temperatures were exceptionally high in 2023/24. Every month from June 2023 to June 2024 set a new record, and September shattered the previous record by 0.5 °C. The 2023 annual average approached 1.5 °C above pre-industrial levels. This results from both long-term warming and internal variability, with the occurrence of an El Nino episode. However the amplitude of the 2023/24 anomalies was remarkable and surprised the scientific community. Here we analyze the rarity of 2023/24 global temperatures from a climate perspective. We show that a 'normal' year 2023 would have roughly equalled the previous annual record, and that the most extreme events of 2023/24 rank among the most extreme since 1940. Our analysis suggests that the 2023/24 event can be reconciled with the long-term trend and an intense, but not implausible, peak of internal variability.