"For many problems involving a fluid and a structure, decoupling of the two is not possible to accurately model the phenomenon at hand, instead the fluid-structure interaction (FSI) problem has to be solved as a coupled problem. This includes a multitude of important problems in biology, medicine and industry, such as the modeling of insect flight, the blood flow in our heart and arteries, human speech, acoustic noise generation in vehicles and wind induced vibrations in bridges and other structures. Major open challenges of computational FSI include; (i) robustness of the fluid-structure coupling, (ii) efficiency and reliability of the computations in the form of adaptivity and quantitative error estimates, and (iii) in the case of high Reynolds number flow the computation of turbulent flow. In this project we address (i)-(iii) by a novel approach which we refer to as a Unified continuum formulation (UCF), where we formulate the fundamental conservation laws for mass, momentum and energy for the combined FSI domain, which is treated as one single continuum, with the only difference being the constitutive relations for the fluid and the structure. The stability problems connected to FSI are related to the exchange of information (stresses and displacements) over the fluid-structure interface, but with UCF we achieve (i) by the global coupling of the conservation laws where the fluid-structure interface is just an interior surface. We achieve (ii)-(iii) by extending to FSI our technology for adaptive finite element methods for turbulent flow with a posteriori error estimation using duality. We typically discretize the equations using a Lagrangian coordinate system for the structure and Arbitrary Lagrangian-Eulerian (ALE) coordinates for the fluid. Preliminary results for the simulation of blood flow are very promising. The computational algorithms are implemented in the open source software FEniCS (www.fenics.org), of which our group is one of the main developers."