Although language itself is unique to humans, many of the sub-components that underlie language processing are shared with other species. A broad comparative approach allows us to tease apart shared elements from unusual (“derived”) characteristics. I will illustrate these principles, first by briefly delving into the neural circuits underlying speech (particularly vocal learning), and then turning to the more challenging problem of syntax (particularly hierarchical syntax). I suggest, based on comparative experimental work carried out within a framework of formal language theory, that humans have a species-typical and early-developing tendency to interpret data in hierarchical terms – a propensity I call “dendrophilia” – that is central to both linguistic and musical syntax and is unusual to our species. In contrast, much of phonology appears to be more widely shared with other mammals and birds (“phonological continuity”). Based on neural and behavioral data, I suggest that our propensity for dendrophilia evolved in a narrowly encapsulated domain, such as motor control and/or social cognition, and was later “exapted” into its domain-general role in human cognition, with far-reaching consequences for our species. Thus, even for unique features like hierarchical syntax, an evolutionary approach can illuminate the precursors for human mechanisms, and give clues to their origins during hominin evolution.