Researchers examining nonverbal communication of emotions are becoming increasingly interested in differentiations between different positive emotional states like interest, relief, and pride. But despite the importance of the voice in communicating emotion in general and positive emotion in particular, there is to date no systematic review of what characterizes vocal expressions of different positive emotions. Furthermore, integration and synthesis of current findings are lacking. In this review, we comprehensively review studies (N = 108) investigating acoustic features relating to specific positive emotions in speech prosody and nonverbal vocalizations. We find that happy voices are generally loud with considerable variability in loudness, have high and variable pitch, and are high in the first two formant frequencies. When specific positive emotions are directly compared with each other, pitch mean, loudness mean, and speech rate differ across positive emotions, with patterns mapping onto clusters of emotions, so-called emotion families. For instance, pitch is higher for epistemological emotions (amusement, interest, relief), moderate for savouring emotions (contentment and pleasure), and lower for a prosocial emotion (admiration). Some, but not all, of the differences in acoustic patterns also map on to differences in arousal levels. We end by pointing to limitations in extant work and making concrete proposals for future research on positive emotions in the voice.