In earthquake engineering, acceleration time histories are the fundamental inputs for the nonlinear analysis of structures as it provides detailed information about the ground motion at a particular location. However, strong motion data are scarce in many seismically active regions around the globe. One of the most seismically active regions is the Himalayan tectonic region, which is constantly subjected to incessant seismic activities. However, the most common and unfortunate aspect is that most of these events remained unrecorded due to a lack of proper instrumentation at those places. Therefore, the limited scope of instrumental records pushes toward using simulated records for engineering applications. However, the earthquake ground motion is highly stochastic and non-stationary owing to its dependence on the complicated source and medium characteristics. Thus, modeling an accelerogram for future earthquakes is difficult. As a result, approaches that generate simulated records that are reasonably simple and time-effective, compatible with a given design spectrum, are particularly popular for both practice and research. Synthetic ground motion data can often be simulated using analytical, numerical, or empirical methods. Analytical approaches, for instance, discrete wavenumber, integral transform, and ray expansion methods, effectively estimate displacement time histories. However, they are only viable in ideal conditions and do not consider the intricate geometry of geological features or the heterogeneity of the earth media. Numerical methods like the finite element method, finite difference method, and spectral finite element method represent the seismic wave propagation in layered media and sedimentary basins to simulate low-frequency time histories. Empirical techniques such as seismological models are relatively simple, time and cost-efficient, and can generate high-frequency time histories. Furthermore, there are various hybrid approaches that combine the strengths of different approaches to estimate ground motions for engineering purposes. Towards this aim, using the ground motion data to estimate slip distribution on the rupture plane for visualizing the rupture process by solving a kinematic inverse problem is most prevalent in literature. Therefore, a review of traditional approaches for the simulation of ground motions and seismic source models is presented in this study.