While the study of ship stability dates back to Archimedes, modern research on vessel dynamics is at the forefront of applied mathematics. Large-amplitude ship motions result in strongly nonlinear, even chaotic behavior. The current trends toward high-speed and unique hullform vessels in commercial and military applications have broadened the need for robust mathematical approaches to studying the dynamics of these innovative ships. The presentations in this minisymposium focus on analytical formulations to model and understand the complicated dynamics leading to vessel phenomena such as capsizing, broaching, and parametric rolling. © Marine Technology.