This talk will give an overview of recent research on wave-ice interactions. Mathematical models (e.g. the NLS and Dysthe equations) are developed to describe wave propagation and attenuation in sea ice. A Hamiltonian point of view is adopted. Various mechanisms (e.g. bending, compression) are taken into account to represent the complex nature of sea ice and its effects on wave dynamics. These predictions range from linear to weakly nonlinear models. Comparison with other existing theories and experimental data will be presented. Direct numerical simulations of nonlinear waves will also be shown, highlighting various configurations with a continuous or fragmented ice cover. This is a compilation of results from joint works with Adilbek Kairzhan, Emilian Parau, Catherine Sulem and Boyang Xu.