In this study we analyze drought features at the European level over the period 1901–2019 using three drought indices: the standardized precipitation index (SPI), the standardized precipitation evapotranspiration index (SPEI), and the self-calibrated Palmer drought severity index (scPDSI). The results based on the SPEI and scPDSI point to the fact that Central Europe (CEU) and the Mediterranean region (MED) are becoming dryer due to an increase in the potential evapotranspiration and mean air temperature, while North Europe (NEU) is becoming wetter. By contrast, the SPI drought does not reveal these changes in the drought variability, mainly due to the fact that the precipitation does not exhibit a significant change, especially over CEU. The SPEI12 indicates a significant increase both in the drought frequency and area over the last three decades for MED and CEU, while SPI12 does not capture these features. Thus, the performance of the SPI may be insufficient for drought analysis studies over regions where there is a strong warming signal. By analyzing the frequency of compound events (e.g., high temperatures and droughts), we show that the potential evapotranspiration and the mean air temperature are becoming essential components for drought occurrence over CEU and MED. This, together with the projected increase in the potential evapotranspiration under a warming climate, has significant implications concerning the future occurrence of drought events, especially for the MED and CEU regions.