Bone tissue is the structural component of the body, which allows locomotion, protects vital internal organs, and provides the maintenance of mineral homeostasis. Several bone-related pathologies generate critical-size bone defects that our organism is not able to heal spontaneously and require a therapeutic action. Conventional therapies span from pharmacological to interventional methodologies, all of them characterized by several drawbacks. To circumvent these effects, tissue engineering and regenerative medicine are innovative and promising approaches that exploit the capability of bone progenitors, especially mesenchymal stem cells, to differentiate into functional bone cells. So far, several materials have been tested in order to guarantee the specific requirements for bone tissue regeneration, ranging from the material biocompatibility to the ideal 3D bone-like architectural structure. In this review, we analyse the state-of-the-art of the most widespread polymeric scaffold materials and their application in in vitro and in vivo models, in order to evaluate their usability in the field of bone tissue engineering. Here, we will present several adopted strategies in scaffold production, from the different combination of materials, to chemical factor inclusion, embedding of cells, and manufacturing technology improvement.