This work deals with phenomena of thermal resistance for metallic surfaces in contact. The main concern of the work is to develop reliable and practical methods for prediction of the thermal contact resistance for various types of surface characteristics under different conditions. In particular, consideration is restricted to the following cases: (i) rough nominally flat surfaces in a vacuum environment; (ii) rough nominally flat surfaces in a fluid environment; (iii) smooth wavy surfaces in a vacuum environment (with either of the following three types of waviness involved; spherical waviness, cylindrical waviness in one direction and cylindrical waviness in two perpendicular directions) and (iv) rough wavy surfaces in a vacuum environment. The problem is divided into three parts: thermal analysis, surface analysis and deformation analysis. The thermal analysis, based upon the proposed models, investigates the analytical solutions for the thermal contact conductance under steady state conditions. It was found convenient, due to the extensive analytical work connected with various models and different methods used here, to present all details of the thermal analysis separately in the appendices. The surface analysis, treating the surfaces as random processes with Gaussian distribution of height, relates the interface geometry to the actual contact area. The method suggested in this analysis has been checked against some autoradiographical experimental data. The deformation analysis, in its two parts, gives dependence between the load supported by the interface and (i) the actual contact area and (ii) the contact spots distribution for rough spherically wavy surfaces, respectively. The result of the first part of