The spatial variation of seismic ground motions denotes the differences in the seismic time histories at various locations on the ground surface. This text focuses on the spatial variability of the motions that is caused by the propagation of the waveforms from the earthquake source through the earth strata to the ground surface, and it brings together the various aspects underlying this complicated phenomenon. Topics covered include: Evaluation of the spatial variability from seismic data recorded at dense instrument arrays by means of signal processing techniques Presentation of the most widely used parametric coherency models, along with brief descriptions of their derivation Illustration of the causes underlying the spatial variation of the motions and its physical interpretation Estimation of seismic ground-surface strains from single station data, spatial array records, and analytical methods Introduction of the concept of random vibrations as applied to discrete-parameter and continuous structural systems on multiple supports Generation of simulations and conditional simulations of spatially variable seismic ground motions Overview of the effects of the spatial variability of seismic motions on the response of long structures, such as pipelines, bridges and dams, with brief descriptions of select seismic codes that incorporate spatial variability issues in their design recommendations This book may serve as a tutorial and/or reference for graduate students, researchers and practicing engineers interested in advancing the current state of knowledge in the analysis and modeling of the spatial variation of the seismic ground motions, or utilizing spatially variable excitations in the seismic response evaluation of long structures.