The foundation of a bridge is an essential structural part linking the bridge with the ground, and its function is to transmit the loads smoothly from piers and abutments to the supporting strata. Unlike foundations of other civil structures, the foundations of bridges are subjected to dynamic loads coming from the superstructures, usually located in water or even deep water and torrents, and have large volumes and self-weights. Consequently, there are special issues related to the design, construction, and maintenance of bridge foundations need to be addressed, especially those relevant to the bridges crossing wide rivers, deep seawaters, and poor geological terrains. Based on the published journal articles and reports, this paper reviews the progresses in the research and development of bridge foundation types, foundation scour, foundation construction, and seismic resistance of foundations. Existing issues in the research and development of bridge foundations are discussed and, based on the discussion, the following topics are suggested for future studies: water-sediment interaction theory and mechanisms of sediment transport for scour at deep water foundations; advanced deep-water foundation structures suitable for China’s sea bedrock; key techniques for positioning and setting of large caisson foundations; and dynamic soil-foundation-structure interaction under earthquake.