Carbon nanotubes (CNTs) possess exceptional mechanical, thermal, and electrical properties, facilitating their use as reinforcements or additives in various materials to improve the properties of the materials. Furthermore, chemically modified CNTs can introduce novel functionalities. In the medical field, biomaterials are expected to be developed using CNTs for clinical use. Biomaterials often are placed adjacent to bone. The use of CNTs is anticipated in these biomaterials applied to bone mainly to improve their overall mechanical properties, for applications such as high-strength arthroplasty prostheses or fixation plates and screws that will not fail. In addition, CNTs are expected to be used as local drug delivery systems (DDS) and/or scaffolds to promote and guide bone tissue regeneration. However, studies examining the use of CNTs as biomaterials still are in the preliminary stages. In particular, the influence of CNTs on osteoblastic cells or bone tissue is extremely important for the use of CNTs in biomaterials placed in contact with bone, and some studies have explored this. This review paper clarifies the current state of knowledge in the context of the relationship between CNTs and bone to determine whether CNTs might perform in biomaterials in contact with bone, or as a DDS and/or scaffolding for bone regeneration.