Fluid-structure interaction problems arise in a wide range of applications, and their numerical simulation is extremely challenging. Eulerian models for fluid-structure interaction [1] have been recently developed to simulate multidimensional problems with large deformations thanks to the implicit treatment of the interface (Level-Set). These models rely on so-called backward characteristics which are defined as the inverse map of the deformations, and correlate the location of a material point to its initial position. Stability is a well-known problem for approaches where fluid and solid are solved at the same time. For this reason, several works have been devoted to the derivation of implicit and semi-implicit schemes. In this presentation, an overview of Eulerian models is given, as well as different approaches to discretize them and improve stability constraints. The presentation closes with a set of 2D and 3D numerical simulations (see Figure 1) to show the potential of these approaches in the context of biological capsules .