Impact-induced seismic vibrations have long been suspected of being an important surface modification process on small satellites and asteroids. In this study, I use a series of linked seismic and geomorphic models to investigate the process in detail. I begin by developing a basic theory for the propagation of seismic energy in a highly fractured asteroid, and I use this theory to model the global vibrations experienced on the surface of an asteroid following an impact. These synthetic seismograms are then applied to a model of regolith resting on a slope, and the resulting downslope motion is computed for a full range of impactor sizes. Next, this computed downslope regolith flow is used in a morphological model of impact crater degradation and erasure, showing how topographic erosion accumulates as a function of time and the number of impacts. Finally, these results are applied in a stochastic cratering model for the surface of an Eros-like body (same volume and surface area as the asteroid), with craters formed by impacts and then erased by the effects of superposing craters, ejecta coverage, and seismic shakedown. This simulation shows good agreement with the observed 433 Eros cratering record at a Main Belt exposure age of $400 \pm 200$ Myr, including the observed paucity of small craters. The lowered equilibrium numbers (loss rate = production rate) for craters less than $\sim 100$ m in diameter is a direct result of seismic erasure, which requires less than a meter of mobilized regolith to reproduce the NEAR observations.This study also points to an upper limit on asteroid size for experiencing global, surface-modifying, seismic effects from individual impacts of about 70-100 km (depending upon asteroid seismic properties). Larger asteroids will experience only local seismic effects from individual impacts.In addition to the study of global seismic effects on asteroids, a chapter is also included which details the impact ejecta plume modeling I have done for the Deep Impact mission to the comet Tempel I. This work will also have direct application to impacts on asteroids, and will be used in the future to refine the cratering history modeling performed thus far.