This paper describes various methods of preparation and characterization of supports (e.g. silicon, polymer, and metal) with grafted polymers and copolymers, which were tailored for biomedical applications. In particular, there are described methods related to preparation of substrates by surface modification leading to incorporation of initiators and, eventually, various polymerization methods yielding complete, dense, and efficient polymer or copolymer coverage with desired arrangement of polymers/copolymers chains, sufficient chains density, and thickness of a polymer layer. Special attention is drawn to the description of manufacturing of patterned polymer stimuli responsive brushes that are sensitive to changes, for example, temperature, pH, hydrophilicity, solvent, and ionic strength. Selected applications of supports containing tethered polymer brushes used as modern materials useful in biosciences, particularly as elements of biosensors, materials for diagnostics, and prostheses, as well as in other areas of micro-technology and nanotechnology are discussed.