The theory of ocean waves has been an important topic of research for more than 150 years due to the signicance of the sea in human history. The motion of waves is a very complex phenomenon and its study has applications in every aspect of our lives. This lecture will explore how methods of mathematical analysis combined with asymptotic theory and numerical simulations can contribute to a better understanding of propagation and interaction of large amplitude ocean waves both at the surface of the ocean and in its interior, in regular situations as well as in extreme events.