Many studies have examined the climatology of individual types of impactful weather systems such as cyclones, fronts and thunderstorms, with some recent studies also considering compound weather systems where more than one type occur at the same time and location. Here we examine compound weather systems based on environmental diagnostics of cyclones, fronts and thunderstorms applied to global reanalysis data for the first time based on multiple decades. Occurrence frequencies are mapped for each type of compound weather system from 1979 to 2020. Results for the double weather system types show that the cyclone and front combination mostly occurs in high-latitude ocean regions, whereas the cyclone and thunderstorm combination as well as the front and thunderstorm combination mostly occur in midlatitude land regions. The triple weather system type of the cyclone, front and thunderstorm combination is rare but tends to occur near the midlatitude east coast and adjacent maritime region of each continent. Thunderstorm-related compound weather systems have occurrence frequency maxima around 35°S and 35°N for ocean regions, with larger occurrence frequencies in the Northern Hemisphere than the Southern Hemisphere, whereas for land regions these occurrence frequencies are smaller in the Northern Hemisphere than the Southern Hemisphere. Long-term trends indicate more thunderstorm-related compound systems in some tropical land regions and midlatitude locations near the east coast of each continent, as well as changes in the Southern Hemisphere extratropics consistent with cyclones moving poleward. This dataset and methodology are also intended to be useful for future studies relevant to a range of disciplines, such as for insight on drivers of hazardous rain, wind and ocean waves through this framework of compound weather systems in regions through the world.