The meshing stage of a Computation Fluid Dynamics (CFD) problem is of crucial importance. In realistic engineering applications, issues arise when dealing with complex, sharp and moving boundaries, removing the possibility of automatic creation of a high quality structured mesh for instance. For Fluid-Structure Interaction (FSI) problems, the standard body-fitted meshing approaches are also limited to low structure deformation and to simple geometries. In light of these limitations, Immersed Boundary Methods (IBMs) have shown to be good alternatives for a broad range of problems. The present work sets out to build a set of numerical methods based on IBMs to simulate both the motion of rigid bodies and the transport of thin flexible solids. This research focuses on the specific area of waste water pumps. Firstly, IBMs are used to provide estimates of the hydrodynamic performances of centrifugal pumps. Secondly, this type of method is used to give a first answer regarding the characterization of the physical mechanism that leads to clogging in such pumps. The numerical tool is coupled to two different solvers for the fluid equations: (i) Navier-Stokes (NS) and (ii) Lattice-Boltzmann (LB). In the NS context, a sharp IBM based on a penalization method is developed and implemented in the open source library OpenFOAM in order to model the flow around rigid bodies. The complete model includes correction of the boundary conditions at the fluid-solid interface to improve the accuracy of the solution and coupling with turbulence models. To model the transport and the deformation of flexible structures, a diffuse penalty based IBM coupled to a solid model based on the variational derivative of the deformation energy is considered. In the LB context, the diffuse IBM available in the open source library Palabos is assessed for one-way coupling problems with rigid bodies. The latter is extended and coupled to the same solid model as above in order to study flexible structures. The capabilities and the accuracy of the two IBMs are assessed and compared with several test cases dealing with rigid bodies. For the sharp NS-IBM, numerical results of academic cases highlight the benefits brought by the corrections of the interface boundary conditions. In engineering cases, the method leads to results in good agreement with experimental data and numerical data from standard body-fitted simulations. Finally, for the IBMs aimed at modelling the flexible structures, both physical approaches compare well with previous numerical models in literature, and are giving promising results regarding the clogging mechanism.