Relativistic quantum mechanical models form an important class of dispersive partial differential equations, with applications ranging from quantum physics to materials science and high-field phenomena. Their numerical simulation presents substantial challenges, including highly oscillatory dynamics, multiscale regimes, spinor coupling, long-time accuracy, and the preservation of intrinsic mathematical structures. This mini-symposium brings together computational and applied mathematicians and computational physicists working on spectral and high-order numerical methods for relativistic quantum models. The focus will be on accurate and efficient discretizations, robust time integration strategies, and rigorous numerical analysis for Dirac-type, Klein-Gordon-type and relativistic Schroedinger-type as well as their related coupled systems. Particular emphasis will be placed on how structure-preserving spectral and high-order methods can improve resolution, stability, and efficiency across different physical regimes.