In the seismic design and analysis of important structures, ground motion time histories are generally required as the input for the conduction of seismic response history analysis. Taking a selected spectrum as the target, the approaches for generating spectral compatible time histories based on artificial or synthetic ground motion and real recorded earthquake ground motion, respectively, are commonly used and discussed in this review. The pure artificial approaches have relative higher effectiveness and computational efficiency, while the approaches by adjusting the real records could simulate the nonstationary in both time domain and frequency domain.