Compound climate events may include concurrent drought and hot events (compound drought-hot events, CDHEs) or consecutive pluvial and hot events (compound pluvial-hot events, CPHEs). The impacts of compound climate extremes can be reduced by developing adaptation strategies which require reliable monitoring of compound climate events and determining the variability and drivers of their risk. The CDHEs can be characterized by leveraging compound indices, such as Standardized Compound Event Indicator (SCEI), Standardized Dry and Hot Index (SDHI), and Blended Dry and Hot Events Index (BDHI), and the CPHEs can be represented via Blended Pluvial and Hot Events Index (BPHI). When Standardized Precipitation Index (SPI) and Standardized Temperature Index (STI) series are divided into different subseries, based on a specific threshold 0, the dependence paradox occurs, i.e., an opposite dependence is exhibited in comparison of the whole SPI-STI series with the segmented SPI-STI subseries. As BDHI considers the dependence between diverse SPI and STI subseries, it can provide more reliable monitoring for CDHEs than SCEI and SDHI over global land masses during the warm season in the 1951–2021 period. Compared with the period of 1951–1986, the frequency, severity, and spatial extent of CDHEs and CPHEs have exacerbated in the period of 1987–2021 over many regions, e.g., western North America, northern South America, western and central Europe, Africa, and eastern Siberia. The risks of CDHEs and CPHEs are intensified by changes in the SPI-STI dependence and high temperature. Moreover, the contributions of drought and pluvial events (i.e., precipitation changes) to risk variations between CDHEs and CPHEs showed complementary spatial patterns. Our findings emphasize that policymakers and stakeholders need to develop more powerful adaptation strategies to mitigate the intensified risks of compound climate extremes.