Abstract: We review several numerical approaches for KdV-type equations, including the generalized KdV and Benjamin-Ono equations as well as the KdV equation with fractional Laplacian. The spatial discretization is achieved by using the Fourier spectral method for fast decay solutions (e.g., in KdV equation), or the spectral method from the Wiener rational basis functions for both fast and slow decay solution cases. Both of these two spatial discretizations preserve the Hamiltonian in the spatial discrete sense. We also discuss the arbitrarily high order Hamiltonian conservative schemes that are constructed by applying the Scalar Auxiliary Variable (SAV) reformulation with the symplectic Runge-Kutta method in the time evolution.