This article reviews the development of artificial bone substitutes from their older single-phase forms to novel multi-phase composites, mimicking the composition and architecture of natural bone tissue. The new generation of bone implants should be bioactive, i.e. they should induce the desired cellular responses, leading to integration of the material into the natural tissue and stimulating self-healing processes. Therefore, the first part of the review explains the common principles of the cell-material interaction and summarizes the strategies how to improve the biocompatibility and bioactivity of the materials by modifying the physico-chemical properties of the material surface, such as surface chemistry, wettability, electrical charge, rigidity, microroughness and especially nanoroughness. The latter has been shown to stimulate preferentially the growth of osteoblasts in comparison with other competitive cell types, such as fibroblasts, which could prevent fibrous tissue formation upon implantation. The second more specialized part of the review deals with materials suitable for bone contact and substitution, particularly novel polymer-based composites reinforced with fibres or inorganic particles and containing bioactive components, such as crystals of hydroxyapatite or other calcium phosphates, synthetic ligands for cell adhesion receptors or growth factors. Moreover, if they are degradable, they can be gradually replaced with a regenerating tissue.