Cell-material interface plays a key role in the interaction of cells with artificial materials designed for construction of body implants or tissue engineering. Physical and chemical properties of the material surface, such as its polarity, wettability, electrical charge and conductivity, roughness and morphology, rigidity or elasticity as well as the presence of various chemical functional groups, strongly influence the cell adhesion. The latter is mediated by adsorption of cell adhesion-mediating molecules (eg: vitronectin, fibronectin, collagen, laminin, fibrinogen) from the serum of the culture medium or body fluids in appropriate spatial conformation or flexibility enabling the accessibility of specific sites on these molecules (eg: certain amino acid sequences or saccharide-based ligands) by adhesion receptors on the cell membrane (eg: integrins). After binding these ligands, the adhesion receptors are recruited into focal adhesion plaques, where they associate with cascades of various structural and signalling molecules, such as cytoskeletal proteins and kinases. By these cascades, the signal provided by the cell-material interaction is delivered to the cell nucleus. It influences the gene expression, and thus the further behavior of cells, manifested by their viability, synthesis of various molecules, proliferation, differentiation, functioning, immune activation, stress adaptation or cell death. This interdisciplinary review involves: (i) physical modifications of the material surface by plasma discharge, irradiation with ions or ultraviolet light and effects of these modifications on the surface wettability, electrical conductivity and formation of chemical functional groups influencing cell adhesion, (ii) deposition of organic or inorganic layers on the material surfaces, especially those nanostructured (eg: nanofibers of fibrin and extracellular matrix molecules, carbon nanoparticles, such as nanodiamonds, fullerenes and nanotubes, nanocomposite metal/C:H layers), (iii) functionalisation of the material surface with amino acids and oligopeptidic ligands for cell adhesion receptors (e.g., GRGDSG), (iv) effect of all these modifications on the extent and strength of adhesion of vascular and bone-derived cells, cell proliferation activity, switch between cell proliferation and differentiation, expression of cell-type specific markers of differentiation and other cell functions.