The field of tissue engineering promises to deliver biological substitutes to repair or replace tissues in the body that have been injured or diseased. The clinical demand for musculoskeletal tissues is particularly high, especially for cartilage and bone defects. Although they are generally considered biologically simple structures, musculoskeletal tissues consist of highly organized three-dimensional networks of cells and matrix, giving rise to tissue structures with remarkable mechanical properties. Although the field of cartilage and bone tissue engineering has progressed significantly in recent years, the development of structurally ordered tissues has not been accomplished. More strategies are needed to ensure that the appropriate cell and matrix organization is being achieved in the engineered tissues. This review emphasizes how different cell types and scaffold designs can be used to modulate tissue properties and engineer more complex tissue structures, with emphasis on cartilage and bone tissues.