The focus of this research is on the development of vibration response-based damage detection in civil engineering structures. Modal parameter-based and model identification-based approaches have been considered. In the modal parameter-based approach, the flexibility and curvature flexibility matrices of the structure are used to identify the damage. It is shown that changes in these matrices can be related to changes in stiffness values of individual structural members. Using this relationship, a method is proposed to solve for the change in stiffness values. The application of this approach is demonstrated on the benchmark problem developed by the joint International Association of Structural Control and American Society of Civil Engineers Structural Health Monitoring task group. The proposed approach is found to be effective in identifying various damage scenarios of this benchmark problem. The effect of missing modes on the damage identification scheme is also studied. The second method for damage identification aims at identifying sudden changes in stiffness for real time applications. It is shown that the high-frequency content of the response acceleration can be used to identify the instant at which a structure suffers a sudden reduction in its stiffness value. Using the Gibb's phenomenon, it is shown why a high-pass filter can be used for identifying such damages. The application of high-pass filters is then shown in identifying sudden stiffness changes in a linear multi-degree-of-freedom system and a bilinear single degree of freedom system. The impact of measurement noise on the identification approach is also studied. The noise characteristics under which damage identification can or cannot be made are clearly identified. The issue of quantification of the stiffness reduction by this approach is also examined. It is noted that even if the time at which the reduction in stiffness happens can be identified, the quantification of damage requires the knowledge of system displacement values. In principle, such displacements can be calculated by numerical integration of the acceleration response, but the numerical integrations are known to suffer from the low frequency drift error problems. To avoid the errors introduced due to numerical integration of the acceleration response, an approach utilizing the unscented Kalman filter is developed to track the sudden changes in stiffness values. This approach is referred to as the adaptive unscented Kalman filter (AUKF) approach. The successful application of the proposed AUKF approach is shown on two multi-degree of freedom systems that experience sudden loss of stiffness values while subjected to earthquake induced base excitation. / Ph. D.