Wet heatwaves can have more impact on human health than hot dry heatwaves. However, changes in these have received little scientific attention. Using the ECMWF Reanalysis v5 reanalysis dataset, wet-bulb temperatures (T (w)) were used to investigate the spatial-temporal variation of wet heatwaves in Eurasia for 1979-2017. Wet heatwaves were defined as three day or longer periods when T (w) was above the 90th percentile of the summer distribution and characterized by amplitude, duration and frequency. Maximum values of amplitude, close to 31 degrees C, occur in the Indus-Ganges plain, the lower Yangtze valley, and the coasts of the Persian Gulf and Red Sea. Significant positive trends in the frequency and amplitude of wet heatwaves have occurred over most of Eurasia though with regional variations. Changes in heatwave amplitude (HWA) are largely driven by changes in summer mean T (w). For Eurasia as a whole, increases in temperature contribute more than six times the impact of changes in relative humidity (RH) to changes in T (w) HWA. Changes in T (w) have a strong dependence on climatological RH with an increase in RH of 1% causing a T (w) increase of 0.2 degrees C in arid regions, and only increasing T (w) by 0.1 degrees C in humid regions. During T (w) heatwaves in Europe, parts of Tibet, India, East Asia and parts of the Arabian Peninsula both temperature and humidity contribute to the increase in T (w), with temperature the dominant driver. During wet heatwaves in part of Russia, changes in humidity are weak and the increase in T (w) is mainly caused by an increase in temperature. In the Mediterranean and Central Asia, RH has fallen reducing the increase in T (w) from general warming.