The Kardar-Parisi-Zhang (KPZ) equation: ∂h/∂t = ν∇²h + (λ/2)(∇h)² + η governs stochastic interface growth. In 1+1D, the stationary height fluctuations follow the Tracy-Widom GUE distribution (not Gaussian!). The roughness exponent α=1/2, dynamic exponent z=3/2. KPZ universality class includes random matrices, TASEP, and directed polymers in random media.