Normal function of the peripheral nerve (PN) is based on morphological integrity and relationship between axons, Schwann cells, and connective sheaths, which depends on the correct development of all these components. Most of the relevant studies in this field were carried out using animal models, since reports on the development of the human PNs from the time of prenatal formation to postnatal development are limited as it is quite difficult to find many nerves in fetuses. In this review paper, we will address the main developmental stages of axons, Schwann cells, and connective tissue sheaths in PNs. Knowledge on the development of PNs and their main components is important for the study of nerve repair and regeneration. This knowledge can be helpful for designing innovative treatment strategies since, like with other organs, the development and regeneration processes share many biological features.