More attention has been paid to studies on the generation, propagation, runup and innudation of tsunami and the tsunami warning methods. The recent progress in tsunamis dynamics and its numerical methods is summarized. The mathematical modeling of tsunamis is reviewed. The high order Boussinesq model and its application in tsunami research are discussed in details, covering numerical simulation of propagation and runup of tsunami on beach and 2004 Indian Ocean Tsunami. Regarding to the tsunami warning metho...