Mathematical physiological models can be applied in medical decision support systems. To do so requires consideration of the necessary model complexity. Models that simulate changes in the individual patient are required, meaning that models should have a complexity where parameters can be uniquely identified at the bedside from clinical data and where the models adequately represent the individual patient’s (patho)physiology. This paper describes the models included in a system for providing decision support for mechanical ventilation. Models of pulmonary gas exchange, respiratory mechanics, acid-base, and respiratory control are described. The parameters of these models are presented along with the necessary clinical data required for their estimation and the parameter estimation process. In doing so, the paper highlights the need for simple, minimal models for application at the bedside, directed toward well-defined clinical problems.