Variability and heterogeneity are intrinsic to many advanced engineering materials—ranging from sedimentary rocks and cementitious composites to fiber- and nano-reinforced metamaterials, porous media, and biological tissues. Accurately quantifying and propagating these uncertainties is critical for reliable computational design, robust material characterization, and meaningful interpretation of experimental data. This Minisymposium brings together recent theoretical advances and computational strategies in Uncertainty Quantification (UQ) for random heterogeneous materials, encompassing both forward propagation of uncertainties through computational models and statistical inverse identification of probabilistic material models. Contributions are invited (but not limited) to the following areas: • Stochastic modeling of material heterogeneity: representation of random fields and microstructures, data-informed microstructure descriptors, multiscale and scale-bridging approaches. • Forward UQ for constitutive behavior: propagation of uncertainties in linear and nonlinear laws (elasticity, plasticity, damage, fracture and other material nonlinearities) under (quasi-)static or dynamic loading. • Statistical inverse problems and model calibration: Bayesian parameter identification of probabilistic models; stochastic optimization and Markov-Chain Monte Carlo (MCMC) methods with experimental-data considerations. • Surrogate and reduced-order modeling: data-driven, physics-informed and probabilistic-learning approaches to accelerate UQ workflows; error estimation, adaptivity, and reliability assessment of surrogates; integration with high-fidelity simulations. • Optimization under uncertainty: material and structural design with performance, reliability or robustness criteria; multi-objective and risk-aware optimization strategies. This Minisymposium aims to (i) showcase advances in UQ methodologies specifically tailored to random heterogeneous materials and their computational modeling, (ii) highlight challenges in modeling, simulating and identifying complex material behavior under uncertainty, and (iii) foster interaction among theoreticians, computational scientists, and experimentalists to advance uncertainty-aware material design and analysis. By bridging together experts in stochastic modeling, numerical simulation, and data-driven methods, we seek to chart new directions for reliable and efficient UQ in materials science and computational mechanics.