Our understanding of the evolution of human speech has been expanded by an increased knowledge of vocal anatomy and physiology in non-human primates. Comparative approaches provide evidence supporting the primate origins of many speech faculties. The descent of the larynx enables the two-tube configuration of the supralaryngeal vocal tract (SVT) in humans; however, this configuration is also found in chimpanzees and macaques. The acoustic properties of voices produced in helium gas support the view that vocalizations are usually produced through SVT resonance, with the sound source generated by vibration of the vocal folds in gibbons and marmosets, as seen in human speech. Nonhuman primates produce a wider range of vocal repertoire than previously thought, reflecting their varied manipulations of the vocal apparatus to modify SVT topology. These species often actively descend the hyoid and larynx to produce calls. This ‘active’ descent is one of the options for SVT modification in non-human primates. However, this is distinct from human speech, where a ‘static’ descended larynx moves in a restricted range during speech. Instead, humans modify SVT configuration by combinations of contraction and relaxation of the tongue muscles, to produce their vocal acoustics. The components of the vocal apparatus act under the constraint of anatomy, and various associations of anatomy and vocal actions are expected to be found in a variety of types of vocalization in non-human primates. Increasing knowledge of their anatomy and physiology promises better understanding of primate origins and of the evolutionary history of physical faculties in human speech.