Several models exist for the simulation of vascular flows; they span from simple circuit models to full three-dimensional ones that take into account detailed features of the blood and of the arterialwall. Eachmodel comeswith both benefits and drawbacks, the main denominator being a compromise between detailed resolution requirements versus computational time. We first present a fluid-structure interaction computationalmodelwhere both the fluid and the structure are three dimensional. In particular, the fluid includes modeling of large eddies by the variationalmultiscalemethod. After time and space discretizations carried out by finite differences and finite elements, respectively, we set up a parallel solver based ondomain decomposition and a FaCSI preconditioner. These simulations allow one to capture details of the flow dynamics and of the structure deformation even in the transitional regime characterizing hemodynamics in the aorta. It takes roughly 10 hours to complete a simulation of one heartbeat with 35 million degrees of freedom on 2048 cores. We then reduce both the model and its numerical complexity. The structural model is simplified to a two-dimensional membrane located at the fluid-structure interface and the fluid computational domain is fixed. For a fixed geometry andmesh, these assumptions allow one to apply proper orthogonal decomposition and generate a space discretization which has only a few dozen degrees of freedom. It is then possible to perform the simulation of one heartbeat on a laptop in less than one second. Themodeling and numerical reduction therefore allows a dramatic reduction of computational time. However, the price to pay comes, on the one hand, in terms of the preparation of a reduced basis specific to the patient and the geometry of the vessel and, on the other hand, with a detriment of certain quantities of interest. For example, when using a finite element discretization with 9 million degrees of freedom, the offline part takes about 12 hours on 720 cores for the example provided in this work; in this case, the flow profiles in the aorta are pretty close to the full three-dimensional