The potential impact of hemodynamic and vascular wall models on the diagnosis, treatment, and well-being of thousands of patients suffering from cardiovascular diseases, is tremendous. Despite the potential impact, it is not straightforward to use these models for individualized diagnosis and intervention planning (model predictive decision support). Major challenges are the adaptation of the models to patient-specific conditions and the necessary uncertainty assessment of the simulated outcome measures. In this manuscript, we will present our view on what is needed to make cardiovascular models suitable for clinical decision support. Hereto, we will first describe how an engineer might support clinical decisions. Secondly, we will give a description of the challenges faced by the engineers. Finally we will introduce an innovative approach in which model personalization is guided by sensitivity analysis, and in which the effect of input uncertainties and model assumptions (acknowledged model errors) on model predictions are considered during model corroboration. The approach is illustrated by two different vascular cases. Hopefully our view will be useful in bringing models from the pre-clinical phase to the clinical phase where they will actually be used for model predictive decision support.