Birdsong shows striking parallels with human speech. Previous comparisons between birdsong and human vocalizations focused on syntax, phonology and phonetics. In this review, we propose that future comparative research should expand its focus to include prosody, i.e. the temporal and melodic properties that extend over larger units of song. To this end, we consider the similarities between birdsong structure and the prosodic hierarchy in human speech and between context-dependent acoustic variations in birdsong and the biological codes in human speech. Moreover, we discuss songbirds’ sensitivity to prosody-like acoustic features and the role of such features in song segmentation and song learning in relation to infants’ sensitivity to prosody and the role of prosody in early language acquisition. Finally, we make suggestions for future comparative birdsong research, including a framework of how prosody in birdsong can be studied. In particular, we propose to analyze birdsong as a multidimensional signal composed of specific acoustic features, and to assess whether these acoustic features are organized into prosody-like structures.