This seminar gives some developments of numerical methods for linear and nonlinear fluid-structure interactions (FSI) with their applications in engineering. The discussions cover the four numerical models: 1) mixed finite element (FE)-substructure-subdomain approach to deal with linear incompressible / compressible FSI involving sloshing / acoustic / explosion waves in fluids; 2) mixed FE-boundary element (BE) model to solve linear water-structure interactions with infinite fluid domain; 3) mixed FE-finite difference (FD) model for nonlinear FSI problems but no separations between fluids and solids; 4) mixed FE-particle method to simulate nonlinear FSI problems with f-s separations as well as breaking waves. The partitioned approach is suggested in base of available fluid and solid codes to separately solve the governing equations of fluid and solid and then to forward step by step through iteration until reached convergence. The selected application examples include air-liquid-shell interactions, LNG ship-water sloshing dynamics; acoustic simulation of air-building interaction system excited by human foot impacts; aircraft landing impacts on water-VLFS interaction system; turbulence flow-body interactions; breaking wave simulations for structure-fluid interactions, etc. The numerical results are compared with the experiment results or numerical data provided by the publications to demonstrate the discussion approaches.