The main purpose of the tsunami generation modelling is to provide an initial condition for various long wave propagation numerical codes. This research topic is substantially underexplored since it is situated on the cross-section of several disciplines such as seismology, hydrodynamics and geophysics. We will begin this presentation by describing classical techniques and mathematical tools currently used to construct the initial condition. Then, we will discuss some shortcomings of traditional approaches. To overcome them, state of the art methods will be introduced. Finally, very recent results on the mud layer influence will be presented.