The simulation of coupled evolutionary partial differential equations (PDEs) with evolving interfaces is a relevant area of research in computational science and engineering. Such problems arise naturally in a broad range of applications, including fluid-structure interaction (FSI), multiphase flows (droplets, cavitating flows, volcanic/magma flows), sorption kinetics (fluid-bubble interactions with adsorption/desorption at interfaces) and phase-change phenomena (melting, solidification). A defining feature of these systems is the presence of interfaces whose geometry and topology evolve over time and may involve large deformations or even topological changes such as merging and splitting. Unfitted boundary methods, such as CutFEM, XFEM, ghost-point methods, immersed boundary methods, fictitious domain methods, offer a powerful alternative to body-fitted or interface-fitted methods, by allowing PDE discretization on fixed background meshes, independently of the interface geometry. This approach simplifies mesh handling, enables robust treatment of complex geometries, and is particularly well-suited to multiphysics coupling and time-dependent interfaces. Recent advances include high-order accurate unfitted discretizations, stabilization techniques for small cut elements, the weak enforcement of boundary and interface conditions via Nitsche’s method, and improved interface tracking approaches (e.g., level set, phase field). Equally crucial is the development of efficient linear solvers tailored to the challenges of unfitted methods. In particular, multigrid solvers adapted to curved and embedded boundaries have shown great promise in maintaining optimal computational complexity, even in the presence of irregular or evolving geometries. These solvers play a crucial role to allow large-scale simulations and real-time computations. This mini-symposium brings together researchers working on mathematical models, numerical methods, and applications of unfitted techniques for PDEs with evolving interfaces. Topics include multiphysics coupling strategies, solver design for unfitted systems, interface representation, and spanning a wide range of multidisciplinary applications, including geophysics, aerospace, biomedicine, energy, microfluidics, and many others.