Local topography conditions may have significant effects on the amplification of ground motion. It may be studied both by analytical and numerical methods. Nevertheless, analytical methods are essential for exploring the physical nature of particular problems, and for checking the accuracy of numerical methods when exact solutions can be found. Local topography is divided into canyons without alluvial layers, canyons with alluvial layers （alluvial valley ）, hill, and composite topography. The researches on the influence of local topography on ground motion are reviewed respectively. Four aspects of research achievements are analyzed and discussed as follows ： （ 1 ） research methods ; （ 2 ） computer medium model; （ 3 ） research level disequilibrium among different local topography;（~）research deficiency. Finally, some ideas and prospects are proposed for later research in this field： seismic response of local topography under the incidence of Raleigh waves is worth further studying; simultaneously seismic response of local topography under the coupling incidence of various waves should be carried out; ground motion of local topography should be studied by nonlinear wave theory and three dimensional nonlinear ground motion numerical simulation should be carried out.[著者文摘]