Formal extensions of the response spectrum method to include spatial seismic effects are reviewed. Two approaches are described in detail: the first based on random vibrations of a simple oscillator under two-component excitations, and the second analyzing multi-column building seismic response. The subjective choice of these two complementing approaches aims at analyzing the phenomenon of spatial seismic vibrations of structures from a broader physical perspective of various wave types propagating among structural supports, with detailed, random vibration sensitivity analysis of a simple structural system still included.