In the last decade, the advent of 3D printing for tissue engineering and regenerative medicine has engendered great interest for those involved in skin repair and regeneration. 3D bioprinting allows spatial distribution of skin cells into predefined custom-made structures to produce living skin mimics on the bench for grafting or drug testing. The key aspect of 3D bioprinting lies in the formulation of printable bioinks serving as matrix mimics to house skin cells, alongside an appropriate combination of cells. In this review, bioink formulations, cell combinations, as well as manufacturing methods exploited to develop 3D bioprinted constructs for skin regeneration are summarized. Issues to do with the selection of suitable materials and cells to ensure the functionality of the resulting skin constructs and fabrication of skin appendages are also addressed.