The whole computational framework to model bioinspired swimmers will be presented. This framework is based on the fictitious domain approach with the use of a (Hierarchical) Cartesian grids. The interfaces between fluids and structures and between two fluids are modeled and tracked by level-set functions. A second order Volume Penalization Method is used to solve the flow at the fluid-structure interface [2], and the Continuous Surface Force is used to model the flow across the bi-fluid interface. The triple line, defined as the intersection the the fluid-structure and bi-fluid interfaces, is computed from the Cox model. For some kind of swimmers, elastic fins are computed from Eulerian elasticity [4] or simplified models. The geometries of the fish-like swimmers are taken from experimental measurements, freely available in the literature or obtained by some biologist collaborators. The imposed deformations are extracted from experimental pictures obtained by high speed cameras. The deformations are either computed in an Eulerian way from optimal mas transport [3] or in a Lagrangian way by deforming the swimmer mesh to fit the actual deformations. Several examples and applications will be presented. The first one is a snake swimming at the water surface from data obtained in the French ANR project DRAGON2. The second one is the dolphin swimming including a jump out of the water [1] using the dolphin geometry freely available in the supplementary materials of [5]. Results are in good agreements with experiments. The numerical solutions complement the experiments with quantitative informations such the swimming efficiency, the energy spent, or the cost of transport. These quantities are indeed difficult or impossible to obtained from experiments. [1] M. Bergmann. Bioinspiration & Biomimetics, 2022. [2] M. Bergmann and J. Hovnanian and A. Iollo. Communications in Computational Physics, 15(5), 2014. [3] M. Bergmann & A. Iollo. J. Comput. Physics, 323, 310-321, (2016). [4] T. Milcent, E. Maitre. Communications in Mathematical Sciences, 14, 2014. [5] H. Tanaka, G. Li, Y. Uchida, M. Nakamura, T. Ikeda, H. Liu, PLOS ONE 14(1), 125,