Physical interactions between solid-solid and solid-fluid domains and coupled interface problems are omnipresent in biomechanics. E.g., they appear in the form of fluid-structure interaction (FSI) between body fluids and external agents [1], or coupling constraints between slender elastica, or contact interactions between deformable elastica of varying dimensions, such as beam-beam, beam-surface, and surface-surface [2]. Inherently, these interface problems are nonlinear and require advanced computational modelling frameworks for their thorough understanding. While state-of-the-art numerical techniques have been proposed to study the FSI phenomenon in biomechanical applications using either monolithic or partitioned schemes [3], mortar-type coupling approaches involving Lagrange multipliers have been adopted to account for contact interactions [4]. For instance, the numerical simulation of two-way FSI coupling between pulsatile blood flow and complex elastic vascular networks spanning multiple spatio-temporal scales is a challenging problem in itself. Another notable example is the high-fidelity numerical simulation of endovascular devices for aneurysm treatment that involves contact interactions. In this mini-symposium, we aim to address the forefront of recent progress, current research, and emerging trends in the computational modelling of nonlinear interface problems in biomechanics. [1] U. Küttler et al., Coupling strategies for biomedical fluid–structure interaction problems, International Journal for Numerical Methods in Biomedical Engineering 26 (2010) 305-321. [2] C. Meier et al., A finite element approach for the line-to-line contact interaction of thin beams with arbitrary orientation, Computer Methods in Applied Mechanics and Engineering 308 (2016) 377-413. [3] K. Surana et al., Mathematical models for fluid-solid interaction and their numerical solutions, Journal of Fluids and Structures 50 (2014) 184-216. [4] I. Steinbrecher et al., A consistent mixed-dimensional coupling approach for 1D Cosserat beams and 2D surfaces in 3D space, Computational Mechanics (2025).