We review computational and weakly nonlinear results for hydroelastic waves travelling at the surface of a fluid covered by a continuous or fragmented ice sheet. The continuous ice-plate model is based on the special Cosserat theory of hyperelastic shells satisfying Kirchhoff's hypothesis. The two-dimensional and three-dimensional nonlinear waves are computed using boundary integral methods and their evolution in time is analysed using a pseudospectral method based on FFT. Internal waves travelling below the ice cover are also discussed. When the ice-plate is fragmented, a new model is proposed by allowing the coefficient of the flexural rigidity to vary spatially.  The attenuation of solitary waves in this case is studied by using time-dependent simulations.