Many human languages have words for emotions such as "anger" and "fear," yet it is not clear whether these emotions have similar meanings across languages, or why their meanings might vary. We estimate emotion semantics across a sample of 2474 spoken languages using "colexification"—a phenomenon in which languages name semantically related concepts with the same word. Analyses show significant variation in networks of emotion concept colexification, which is predicted by the geographic proximity of language families. We also find evidence of universal structure in emotion colexification networks, with all families differentiating emotions primarily on the basis of hedonic valence and physiological activation. Our findings contribute to debates about universality and diversity in how humans understand and experience emotion.