This study focuses on developing structural health monitoring techniques to detect damage in deepwater risers subjected to vortex-induced vibration (VIV), and studying vibration control strategies to extend the service life of offshore structures. Vibration-based damage detection needs both responses from the undamaged and damaged deepwater risers. Because no experimental data for damaged deepwater risers is available, a model to predict the VIV responses of deepwater risers with given conditions is needed, which is the forward problem. In this study, a new three dimensional (3D) analytical model is proposed considering coupled VIV (in-line and cross-flow) for top-tensioned riser (TTR) with wake oscillators. The model is verified by direct numerical simulations and experimental data. The inverse problem is to detect damage using VIV responses from the analytical models with/without damage, where the change between dynamic properties obtained from riser responses represents damage. The inverse problem is performed in two steps: blind identification and damage detection. For blind identification, a wavelet modified second order blind identification (WMSOBI) method and a complex WMSOBI (CWMSOBI) method are proposed to extract modal properties from output only responses for standing and traveling wave vibration, respectively. Numerical simulations and experiments validate the effectiveness of proposed methods. For damage detection, a novel weighted distribution force change (WDFC) index (for standing wave) and a phase angle change (PAC) index (for traveling wave) are proposed and proven numerically. Experiments confirm that WDFC can accurately locate damage and estimate damage severity. Furthermore, a new fatigue damage estimation method involving WMSOBI, S-N curve and Miner's rule is proposed and proven to be effective using field test data. Vibration control is essential to extend the service life and enhance the safety of offshore structures. Literature review shows that semi-active control devices are potentially a good solution. A novel semi-active control strategy is proposed to tune the damper properties to match the dominant frequency of the structural response in real-time. The effectiveness of proposed strategy in vibration reduction for deepwater risers and offshore floating wind turbines is also validated through numerical studies.