Extreme climate events play an important role in studies of long-term climate change. As the Earth's Third Pole, the Tibetan Plateau (TP) is sensitive to climate change and variation. In this study on the TP, the spatiotemporal changes in climate extreme indices (CEIs) are analyzed based on daily maximum and minimum surface air temperatures and precipitation at 98 meteorological stations, most with elevations of at least 4000 m above sea level, during 1960–2012. Fifteen temperature extreme indices (TEIs) and eight precipitation extreme indices (PEIs) were calculated. Then, their long-term change patterns, from spatial and temporal perspectives, were determined at regional, eco-regional and station levels. The entire TP region exhibits a significant warming trend, as reflected by the TEIs. The regional cold days and nights show decreasing trends at rates of −8.9 d (10 yr)^-1 (days per decade) and −17.3 d (10 yr)^-1, respectively. The corresponding warm days and nights have increased by 7.6 d (10 yr)^-1 and 12.5 d (10 yr)^-1, respectively. At the station level, the majority of stations indicate statistically significant trends for all TEIs, but they show spatial heterogeneity. The eco-regional TEIs show patterns that are consistent with the entire TP. The growing season has become longer at a rate of 5.3 d (10 yr)^-1. The abrupt change points for CEIs were examined, and they were mainly distributed during the 1980s and 1990s. The PEIs on the TP exhibit clear fluctuations and increasing trends with small magnitudes. The annual total precipitation has increased by 2.8 mm (10 yr)^-1 (not statistically significant). Most of the CEIs will maintain a persistent trend, as indicated by their Hurst exponents. The developing trends of the CEIs do not show a corresponding change with increasing altitude. In general, the warming trends demonstrate an asymmetric pattern reflected by the rapid increase in the warming trends of the cold TEIs, which are of greater magnitudes than those of the warm TEIs. This finding indicates a positive shift in the distribution of the daily minimum temperatures throughout the TP. Most of the PEIs show weak increasing trends, which are not statistically significant. This work aims to delineate a comprehensive picture of the extreme climate conditions over the TP that can enhance our understanding of its changing climate.