1. Introduction -- 2. AUV Modelling -- 3. Receding Horizon Optimization for Integrated Path Planning and Tracking Control of an AUV -- 4. Lyapunov-Based Model Predictive Control for Dynamic Positioning and Trajectory Tracking Control of an AUV -- 5. Multi-Objective Model Predictive Control for Path Following Control of an AUV -- 6. Efficient Implementation Algorithms for NMPC Trajectory Tracking Control of an AUV -- 7. Distributed Lyapunov-based Model Predictive Formation Tracking Control for AUVs Subject to Disturbances -- 8. Conclusions and Future Work.