The structural response of buildings to earthquake shaking is of critical importance for seismic design purposes. Research on the relationship between earthquake ground motion intensity, building response, and seismic risk is ongoing, but not yet fully conclusive. Often, probability demand models rely on one ground motion intensity measure (IM) to predict the engineering demand parameter (EDP). The engineering community has suggested several IMs to account for different ground motion characteristics, but there is no single optimal IM. For this study, we compile a comprehensive list of IMs and their characteristics to assist engineers in making an informed decision. We discuss the ground motion selection process used for dynamic analysis of structural systems. For illustration, we compute building responses of 2D frames with different natural period subjected to more than 3500 recorded earthquake ground motions. Using our analysis, we examine the effects of different structural characteristics and seismological parameters on EDP-IM relationships by applying multi-regression models and statistical inter-model comparisons. As such, our results support and augment previous studies and suggest further improvements on the relationship between EDP and IM in terms of efficiency and sufficiency. Finally, we provide guidance on future approaches to the selection of both optimal intensity measures and ground motions using newer techniques.