Bridges are a vital infrastructure component of the transportation networks in both rural and urban areas. Damaged or destroyed bridges can affect the reliability and resilience of transportation networks that are critical to human life, economical activities, and the social sustainability at large. Understanding how natural hazards affect the life-cycle performance of bridge systems will lead to improved preparedness prior to extreme disasters and benefit the society ultimately. Among many natural events, flood-induced foundation scour has been recognized as a leading cause of bridge failure in the United States. The distinct feature of flood-induced scour is that it may last during the rest of bridge's service life once it is formed around a bridge foundation. Intuitively, the threat may be potentially more severe if the permanent scour is combined with other hazards, such as earthquakes. However, the combined effects of such multiple hazards are not clearly understood to date. It is thus meaningful to investigate the effects of multi-hazard earthquake and scour on the seismic performance of river-crossing bridges. The general objective of this dissertation is to assess the seismic vulnerability of bridge structures considering flooding-induced scour in a general multi-hazard context. To meet this objective, five related research problems are defined in this dissertation. Correspondingly, scientific answers and technical solution frameworks are developed in this dissertation. The dissertation directly contributes to the multi-hazard assessment methodology with an emphasis in flood-induced scour and earthquake hazards. Specifically, the dissertation directly resolves the practical challenge of evaluating the effects of bridge scour on the seismic performance of river-crossing bridges in terms of theoretical frameworks, numerical procedures, and case study-based findings. Future research directions along the line of multi-hazard bridge performance research with an emphasis of hydro- and seismic-impacts are pointed at the end of the dissertation.