The mathematical modeling of design earthquake loads for engineering structures, such as large dams, tall structures, frame structures and long-span bridges within deterministic and probabilistic frameworks is described. Modern methods of time-variant structural reliability analysis including first-order reliability methods (FORM) and response surface modeling (RSM) could be employed in arriving at critical non-stationary earthquake excitation models for linear, nonlinear and parametrically excited structures. This new contribution is carried out by integrating methods of structural reliability analysis, response surface method, nonlinear dynamics and nonlinear optimization programming (SQP) to arrive at a new framework that leads to acceptable random seismic inputs for engineering structures. Numerical illustrations on modeling deterministic and random (single/multi components) design earthquake loads for an earth dam, a stack-like structure and a steel frame structure are provided. The study also models spatially-varying earthquake ground motions for extended structures by computing optimal auto- and cross-power spectral density (PSD) functions in the probabilistic approach and spatially-varying time histories in the deterministic approach for an idealized two-span bridge structure.