The response of buildings to ground-borne vibration is governed by many physical phenomena. Not least of these is the dynamic soil-structure interaction (SSI) that exists between the various components of the system. The majority of existing models assume that the interaction between a railway tunnel and a building's foundation is negligible, with the two sub-systems behaving as though they are uncoupled; other components of SSI associated with the foundation and building are accounted for to varying degrees, often with little justification. This paper aims to further our understanding of the SSI between an underground railway tunnel and a nearby building. The response of a typical multi-storey building founded on piles is considered, over the frequency range typically associated with perceptible vibration. A comprehensive numerical model is used to capture the fully-coupled, three-dimensional behaviour of the tunnel-foundation-building system, to investigate the relative significance of four fundamental components of SSI when predicting the overall vibration levels within the building. The effects of building location, relative to the tunnel, pile length and foundation configuration are investigated. Three further building models, of varying complexity, are used to explore the extent to which simplified models can capture the fundamental SSI of the system. The conclusions appear promising for the development of simplified models, particularly those aimed at making overall or relative predictions of building vibration levels to guide the design of mitigation measures.