Language and music are universal human traits, raising the question for their evolutionary origin. This chapter takes a comparative perspective to address that question. It examines similarities and differences between humans and non-human animals (mammals and birds) by addressing whether and which constituent cognitive components that underlie the human ability for language and music can be found in non-human animals. It first provides an introduction to the nature and meaning of vocalizations and non-vocal communicative sounds in non-human animals. Next it reviews experimental and observational evidence of animal perception of various frequency and temporal dimensions of sounds. Many animal species show perceptual and cognitive abilities to distinguish between or to generalize auditory stimuli. This includes evidence of the presence of one or more of the constituent cognitive components on which the human abilities for language and music are based, or that may have served as precursors for these components. At the same time, there are also important differences among animal species in their abilities. Hence contrasts are not limited to those between humans and other animal species. The differences between humans and other species, as well as those among non-human species, might result from specific biases and the weight or priority certain species give to attending to certain features of an acoustic signal, or because different species use particular mechanisms to different degrees.