Heart and vessel diseases, or cardiovascular diseases (CVDs), are globally the main cause of mortality and morbidity. The blood flow plays an important role in their occurrence and progression. Therefore, knowledge of the blood flow is of key importance to reduce and threat these diseases. This knowledge requires both high-quality data and an insightful visual representation. Using advanced imaging techniques, for example phase-contrast magnetic resonance imaging (PC-MRI), the blood flow in a patient can be measured. This technique provides patient-specific 3D data over time, that is, for every measured position, a so-called voxel, the velocity of the blood is measured in all three directions. From these three values per voxel, a vector can then be reconstructed that tells us how fast and in which direction the blood was flowing at the measured location. By doing this for multiple moments one can obtain this data throughout a heart cycle. Since this data is three dimensional and changing over time generating a visual representation of this data is challenging for multiple reasons. One such reason is occlusion where part of the visualization is hidden by the rest of the visualization. Another is visual clutter where the visualization is ``too busy'' and therefore unclear. Moreover, the measured data is subject to noise and artefacts which further hinder the visualization. In this dissertation, novel visualization approaches are presented that address these and other visualization challenges of PC-MRI data. Besides PC-MRI data, blood flow data can be created using computer simulation models, for example using computational fluid dynamics (CFD) models, that are based on physical models. For this usually the shape of the blood vessel is measured using imaging techniques which is in turn used to simulate the blood flow inside the vessel. However, both measuring and modelling the blood flow have their own advantages and disadvantages. For example, PC-MRI measurements suffer from the inevitable effects of measurement noise which causes the data to deviate from the actual blood flow in the patient. Simulations, on the other hand, require detailed input information and are based on model assumptions, and hence result in data that is not always representative for the patient, however, the resulting data does correspond to the physical model. In addition to visualization approaches, this work also presents novel methods that combine PC-MRI measurements and simulations such that the resulting data is both physically-plausible and patient-specific.