Osteosarcoma (OS) is the most common primary malignant tumor of bone that mainly affects children and adolescents. The currently available therapies are not effective and the search for new OS anticancer drugs is extremely urgent. Understanding the mechanisms that underlie the tumor progression, invasion, and metastasis is an essential step toward effective cancer therapies. Tissue engineering has given a great contribution to the development of reliable and cost-effective platforms for drug screening and validation through 3D in vitro models that more faithfully mimic the in vivo pathophysiology than conventional 2D models. The progress in the field of functional and biomimetic biomaterials in the development of 3D tissue models has provided tools for a close recapitulation of the highly complex and dynamic tumor microenvironment. This review focuses on the most recent advances in 3D in vitro osteosarcoma models, highlighting the crucial role of the extracellular matrix and stromal cells in tumor progression, how they contribute to drug resistance and disease prevalence, and the future pathways toward an effective and personalized model for drug screening and validation.