We present detailed state of the art of statistical kinematic source models. The literature constitutes detailed first- and second-order characterization and the corresponding implementation in random field generations. The notable details include scaling relations, non-Gaussianity, and non-stationarity. The simplicity in the representation of kinematic slip fields has also paved the way to easy numerical implementation. Further, computational facility advancements have aided in realistic real-time simulation. Hence, these models can be suitably utilized to obtain more reliable synthetic ground motions and resultant hazards. This work also demonstrates the implementation of a non-Gaussian slip field in physics-based simulation for the Indo-Gangetic basin and studies the corresponding basin amplification.