Three categories of membrane oxygenators are considered: passive flow, secondary flow induced by the mainstream, secondary flow induced by an external application of energy. The current status of mathematical methods for analysis of fluid mechanics, O2 and CO2 exchange for these categories are briefly reviewed. Emphasis is given to approximate methods for calculation of gas exchange. Practical methods for experimental design optimization studies are outlined; these methods are extended to evaluation of O2 and CO2 exchange in clinical operation. A new method for estimation of internal ventilation and perfusion maldistribution and diffusion resistance is described. A brief assessment of blood damage in clinical application of the oxygenator is presented from the point of view of deterioration of gas exchange performance.