The subject of dynamic soil-structure interaction (SSI) is fundamental to the design of structures and foundations to withstand dynamic events such as earthquakes, explosions and vibrations from traffic, wind, waves and machinery. With the tools of modern experimental and computational methods, a critical evaluation of current concepts and capabilities for the dynamic characterization of both surface foundations and embedded piles in granular soils is the first target. Well suited for this kind of fundamental study, a variety of scaled-model surface and pile foundations are designed and tested in a large geotechnical centrifuge using dynamic forced excitations. Used as a rigorous theoretical setting for synthesis of the measurements, an advanced boundary element code is extended to address some complex aspects of three-dimensional boundary value problems. Through the integrated study, significant analytical, numerical and physical insights are gained, and a number of fundamental resolutions and milestones are realized. On the analytical side, they include the identification and solution of a problem related to slender elements in the boundary element method, and a new class of elements for discretization methods in general. On the physical side, they encompass the development and generation of a significant experimental database on soil-structure interaction, as well as the implementation and validation of the hybrid-mode dynamic test method for surface and deep foundations. As a new framework of understanding for theoretical research and engineering practice, these developments are used to formulate (i) an advanced inclusion model for surface foundations under multi-directional loading, and (ii) a comparable theory for the corresponding pile problem, both of which can rationally explain many key experimental observations