Human vocalization systems are characterized by complex structural properties. They are combinatorial, based on the systematic reuse of phonemes, and the set of repertoires in human languages is characterized by both strong statistical regularities - universals--and a great diversity. Besides, they are conventional codes culturally shared in each community of speakers. What is the origins of the forms of speech? What are the mechanisms that permitted their evolution in the course of phylogenesis and cultural evolution? How can a shared speech code be formed in a community of individuals? This chapter focuses on the way the concept of self-organization, and its interaction with natural selection, can throw light on these three questions. In particular, a computational model is presented and shows that a basic neural equipment for adaptive holistic vocal imitation, coupling directly motor and perceptual representations in the brain, can generate spontaneously shared combinatorial systems of vocalizations in a society of babbling individuals. Furthermore, we show how morphological and physiological innate constraints can interact with these self-organized mechanisms to account for both the formation of statistical regularities and diversity in vocalization systems.