Recently, ‘medicine in silico’ has been strongly encouraged due to ethical and legal limitations related to animal experiments and investigations conducted on patients. Computer models, particularly the very complex ones (virtual patients—VP), can be used in medical education and biomedical research as well as in clinical applications. Simpler patient-specific models may aid medical procedures. However, computer models are unfit for medical devices testing. Hybrid (i.e., numerical–physical) models do not have this disadvantage. In this review, the chosen approach to the cardiovascular system and/or respiratory system modeling was discussed with particular emphasis given to the hybrid cardiopulmonary simulator (the artificial patient), that was elaborated by the authors. The VP is useful in the education of forced spirometry, investigations of cardiopulmonary interactions (including gas exchange) and its influence on pulmonary resistance during artificial ventilation, and explanation of phenomena observed during thoracentesis. The artificial patient is useful, inter alia, in staff training and education, investigations of cardiorespiratory support and the testing of several medical devices, such as ventricular assist devices and a membrane-based artificial heart.