The Discrete Variational method for molecules and clusters (DVM), in the framework of Density Functional theory, is described in detail. The numerical grids utilized, basis functions and potential are discussed, as well as spin-polarization for magnetic systems, total energy and dynamics. The relativistic version of the DV method is also described. Applications to large molecules range from porphyrins, a transition metal complex of thiophene, the circular molecule "ferric wheel" containing ten Fe atoms and other transition metal complexes investigated by fragments. Examples of relativistic calculations are given for 5d-metal complexes. Calculations for solids, represented by embedded clusters as large as 65-75 atoms, include transition metals, perovskites, silicates and rare-earth borocarbides. Properties investigated and analysed are structural, optical, hyperfine, magnetic and superconducting. The electronic structure and chemical bonds are also studied by Mulliken populations and charges, bond order, density of states and spin density maps; results are related to experimentally observed characteristics.