In many physiological or pathological situations, the interpretation of BOLD signals remains elusive as the intimate link between neuronal activity and subsequent flow/metabolic changes is not fully understood. During the past decades, a number of biophysical models of the neurovascular coupling have been proposed. It is now well-admitted that these models may bridge between observations (fMRI data) and underlying biophysical and (patho-)physiological mechanisms (related to flow and metabolism) by providing mechanistic explanations. In this study, three well-established models (Buxton's, Friston's and Sotero's) are investigated. An exhaustive parameter sensitivity analysis (PSA) was conducted to study the marginal and joint influences of model parameters on the three main features of the BOLD response (namely the principal peak, the post-stimulus undershoot and the initial dip). In each model, parameters that have the greatest (and least) influence on the BOLD features as well as on the direction of variation of these features were identified. Among the three studied models, parameters were shown to affect the output features in different manners. Indeed, the main parameters revealed by the PSA were found to strongly depend on the way the flow(CBF)-metabolism(CMRO(2)) relationship is implemented (serial vs. parallel). This study confirmed that the model structure which accounts for the representation of the CBF-CMRO(2) relationship (oxygen supply by the flow vs. oxygen demand from neurons) plays a key role. More generally, this work provides substantial information about the tuning of parameters in the three considered models and about the subsequent interpretation of BOLD signals based on these models.