Modelling is a key element to improve the performance of engine control systems, but many factors like non-linearity and complexity complicate the derivation of sufficiently precise physical models. This motivates an increasing interest in data based models. Linear models can successfully represent the engine operation in some reduced regions, but tend to fail when large operating regions must be considered. This motivates the interest in deriving and using gain scheduling models or their natural extension, the linear parameter varying (LPV) models. In this article we propose to model the air path of diesel engines using input-output LPV models with a physically motivated structure and parameters estimated from data. These models are shown to combine good precision with simplicity and allow the systematic design of optimal and robust control systems, and can be determined in a very short time if sufficient data are available.