High-dimensional problems are ubiquitous in scientific computing, arising in kinetic theory, quantum physics, multiscale flow and transport, and inverse problems, among others. Theories and numerical algorithms faces fundamental challenges due to the curse of dimensionality, demanding novel algorithmic frameworks and rigorous mathematical foundations. This minisymposium brings together researchers to present recent advances in structure-exploiting numerical methods for high-dimensional problems, spanning low-rank tensor approximations, model order reduction, multiscale techniques, AI-based surrogate modeling and PDE theories. These contributions highlight emerging algorithmic frameworks and mathematical theories that overcome the computational barriers of the curse of dimensionality across diverse scientific applications.