The motion of insects, birds or fish can be described as a fluid-structure interaction problem, in which one or more deformable bodies are immersed in a fluid. The dynamics of the bodies is a direct result of their hydrodynamic interaction with the surrounding fluid, which is driven by their deformation (active or passive). As a consequence, the resulting problem is a highly non-linear problem consisting of the coupling between the equations of the fluid motion and the equations of motion of the bodies. Moreover, these bodies are usually geometrically complex: they may have mobile appendages and/or they may be deformable and subject to large deformations. This geometrical variability/complexity poses additional problems when modelling this kind of problems, since the fluid-solid interface changes with time. In our group, we have developed a methodology to study bioinspired fluid structure interaction problems (https://doi.org/10.1016/j.jfluidstructs.2022.103519). In the talk we will briefly introduce the methodology and to illustrate its capabilities two applications will be presented. First, we will report simulations of the flow around spanwise-flexible wings in forward flight (https://doi.org/10.1017/jfm.2023.308). This is a rich problem which involves fluid-structure resonance and aerodynamic tailoring. Second, we will discuss hydrodynamic interactions of self-propelled flappers in tandem configuration (https://doi.org/10.1017/jfm.2021.918). In this problem, we will show how the performance of the follower flapper is influenced by hydrodynamic interactions with the wake of the leader flapper.