The “immersed boundary method (IBM)” is considered to be the most efficacious and versatile technique to solve flow problems associated with intricate geometries. The first part of this review examines recent advancements in IBM, essential for the simulation of “fluid–structure interactions (FSIs)” in sophisticated systems. This review highlights significant developments in turbulence modeling, adaptive mesh refinement, and complex geometric simulations, demonstrating IB methods’ capacity to seamlessly integrate arbitrary geometries into structured computational grids while preserving computational efficiency. Various IB techniques are analyzed for enforcing boundary conditions on dynamic immersed boundaries, with notable breakthroughs in managing velocity discontinuities, spurious oscillations, and large-scale deformations. Recent findings illustrate the versatility of IB methods, with applications encompassing biological fluid dynamics, turbulent multiphase flows, and cavitating flows. These innovations not only enhance computational performance but also address evolving challenges across engineering and scientific fields, establishing IB methods as a robust tool for resolving complex, multidisciplinary problems with high accuracy and efficiency.

This article discusses contemporary strategies to deal with immersed boundary (IB) frameworks useful for analyzing flow–structure interaction in complex settings. It focuses on immense advancements in various fields: biology, oscillation of structures due to fluid flow, deformable materials, thermal processes, settling particles, multiphase systems, and sound propagation. The discussion also involves a review of techniques addressing moving boundary conditions at complex interfaces. Evaluating practical examples and theoretical challenges that have been addressed by these frameworks are another focus of the article. Important results highlight the integration of IB methods with adaptive mesh refinement and high-order accuracy techniques, which enormously improve computational efficiency and precision in modeling complex solid–fluid interactions. The article also describes the evolution of IB methodologies in tackling problems of energy harvesting, bio-inspiration propulsion, and thermal-fluid coupling, which extends IB methodologies broadly in many scientific and industrial areas. More importantly, by bringing together different insights and paradigms from across disciplines, the study highlights the emerging trends in IB methodologies towards solving some of the most intricate challenges within the technical and scientific domains.