The penetration to geological shield occurs in many situations at various velocities and scales, for example, meteor-cratering, pile driving, falling of objects from high-rise building construction, and debris/fragments from failed components. The soil media is an efficient energy dissipation system and effective shock protection shield. Impact circumstances are currently getting widespread attention. A lot of research has been done on soil media for impact and penetration. The phenomenon of dynamic penetration in heterogeneous particulate soil medium is very complex and the target soil media under dynamic impact especially under high speed and deep penetration neither behave completely as solid nor as liquid. The topics of recent research interest in the field of penetration to soil media and their significant findings are critically reviewed in the present study. The dedicated review of analytical, empirical, experimental, and computational methods to predict the response of soils media-impacting objects to penetration is presented. The emerging challenges in fundamental research of penetration into soil media are outlined and it is an attempt to formulate the future research directions in the field of soil media penetration.