In the last decade, interest in the field of three-dimensional (3D) bioprinting has increased enormously. 3D bioprinting combines the fields of developmental biology, stem cells, and computer and materials science to create complex bio-hybrid structures for various applications. It is able to precisely place different cell types, biomaterials and biomolecules together in a predefined position to generate printed composite architectures. In the field of tissue engineering, 3D bioprinting has allowed the study of tissues and organs on a new level. In clinical applications, new models have been generated to study disease pathogenesis. One of the most important components of 3D bio-printing is the bio-ink, which is a mixture of cells, biomaterials and bioactive molecules that creates the printed article. This review describes all the currently used bio-printing inks, including polymeric hydrogels, polymer bead microcarriers, cell aggregates and extracellular matrix proteins. Amongst the polymeric components in bio-inks are: natural polymers including gelatin, hyaluronic acid, silk proteins and elastin; and synthetic polymers including amphiphilic block copolymers, PEG, poly(PNIPAAM) and polyphosphazenes. Furthermore, photocrosslinkable and thermoresponsive materials are described. To provide readers with an understanding of the context, the review also contains an overview of current bio-printing techniques and finishes with a summary of bio-printing applications.