This is the Review paper studied the combined effects of earthquake-triggered landslides and ground shaking on sloping ground. Sikkim earthquake of September 18,2011 was the first earthquake in India which exposed the RC frame building on hill slopes to ground shaking and performance of such buildings in this rather moderate ground shaking was far from satisfactory. Due to scarcity of flat land in hilly areas, majority of the building is constructed on the hill slopes with regular structural configuration having foundations at different levels. Such buildings pose special structural and constructional problems. Dynamics characteristic of hill buildings (the term has been used in this paper for buildings located on hill slopes) are significantly different in both horizontal and vertical directions, results in center of mass and center of stiffness of a story not coinciding with each other and not being on a vertical line for different floors. When subjected to lateral loads, these buildings are generally subjected to significant torsional response. The various floors of such buildings step backs towards hill slope and at the same time buildings may have setbacks also. Most of the studies agree that the buildings resting on sloping ground has higher displacement and base shear compared to buildings resting on plain ground and the shorter column attracts more forces and undergo damage when subjected to earthquake. Step back building could prove more vulnerable to seismic excitation..