This review briefly outlines the history and possibilities of bone reconstruction using various types of artificial materials, which allow interaction with cells only on the surface of the implant or enable ingrowth of cells inside the material. Information is also provided on the most important properties of bone cells taking part in bone tissue development, and on diseases and regeneration. The most common cell types used for testing cell-material interaction in vitro are listed, and the most commonly used approaches to this testing are also mentioned. A considerable part of this review is dedicated to the physical and chemical properties of the material surface, which are decisive for the cell-material interaction, and also to modifications to the surface of the material aimed at integrating it better with the surrounding bone tissue. Special attention is paid to the effects of nanoscale and microscale surface roughness on cell behaviour, to material surface patterning, which allows regionally-selective adhesion and growth of cells, and also to the surface chemistry. In addition, coating the materials with bioactive layers is examined, particularly those created by deposition of fullerenes, hybrid metal-fullerene composites, carbon nanotubes, nanocrystalline diamond films, diamond-like carbon, and nanocomposite hydrocarbon plasma polymer films enriched with metals.