This chapter highlights the effectiveness of the splitting scheme approach in analyzing fluid-structure interaction (FSI) problems. The Lie operator splitting method, previously demonstrated for both linear and nonlinear FSI models, has proven robust and adaptable, enabling the constructive existence of weak solutions for complex coupled systems. Its versatility extends to physically significant applications, including more intricate FSI scenarios. The discussion sets the stage for further developments in this book by showcasing how this framework can be extended to analyze advanced FSI models of practical relevance.