In this article we introduce computer models that have been developed in the past to determine the concentration of metabolic gases, the oxygen and carbon dioxide, along the pulmonary circulation. The terminal concentration of these gases in the arterial blood is related with the total change of the partial pressure of the same gases in the alveoli for the time beginning with inspiration and ending with expiration. It is affected not only by the ventilation-perfusion ratio and the gas diffusion capacity of the lung membrane but also by the pulmonary defect such as shunt, dead space, diffusion impairment and ventilation-perfusion mismatch. Some pathological pulmonary symptoms such as ARDS and CDPD can be understood through the mathematical models of these pulmonary dysfunctions. Quantitative study on the blood oxygenation process using various computer models is therefore of foremost importance in order to monitor not only the pulmonary health but also the cardiac output and cell metabolism. Reviewed in this paper include the basic and advanced methods that enable numerical study on the gas exchange and on the arterial oxygenation process, which might depend on the various heart and lung physiological conditions listed above.