Phenomena such as cyclones, fronts and thunderstorms can cause extreme weather in various regions throughout the world. Although these phenomena have been examined in numerous studies, they have not all been systematically examined in combination with each other, including in relation to extreme precipitation and extreme winds throughout the world. Consequently, the combined influence of these phenomena represents a substantial gap in the current understanding of the causes of extreme weather events. Here we present a systematic analysis of cyclones, fronts and thunderstorms in combination with each other, as represented by seven different types of storm combinations. Our results highlight the storm combinations that most frequently cause extreme weather in various regions of the world. The highest risk of extreme precipitation and extreme wind speeds is found to be associated with a triple storm type characterized by concurrent cyclone, front and thunderstorm occurrences. Our findings reveal new insight on the relationships between cyclones, fronts and thunderstorms and clearly demonstrate the importance of concurrent phenomena in causing extreme weather.