In modern engineering applications, much of the overall effort invested in finite element analysis is often devoted to geometric modeling and the transition from computer-aided design (CAD) to analysis-suitable models. Fictitious domain methods were introduced already in the early 1960s to avoid the need for body-fitted mesh generation. Since then, many variants of these appealing ap-proaches have been suggested, like embedded domain and immersed boundary methods or special implementations of the extended finite element method. They share with Isogeometric Analysis: "To support better design-through-analysis by closely coupling geometric modeling and numerical simulation." This mini symposium will focus on advanced immersed/embedded/unfitted meth-ods dedicated to CFD and FSI problems, including possible interactions with other physical fields (e.g., heat, multi-phase flow, etc.). The topics of this mini symposium will range from modeling aspects, including the coupling of analysis and CAD, mathematical analysis, stabilization, pre-conditioning, integration of cut cells, adaptivity, and implementational issues to the efficient solution of complex engineering problems. It will address low and higher-order unfitted discretization approaches, CutFEM, the Finite Cell Method, the Shifted Boundary Method (SBM), immersogeometric analysis, and other combina-tions with the Isogeometric Analysis. The goal is to bring together experts from academia and industry to discuss the most recent advances and emerging research directions in this field.