Sandwich panels are widely used in the design of unmanned satellites and, in addition to having a structural function, can often serve as shielding, protecting the satellites’ equipment from hypervelocity impacts (HVI) of orbital debris and micrometeoroids. This paper provides a comprehensive review of experimental studies in the field of HVI on sandwich panels with honeycomb- and open-cell foam cores, as well as an examination of available predictive models for the assessment of the panels’ ballistic limits. The emphasis of the review is placed on: (i) identifying gaps in the existing experimental database and the appropriate directions for its further expansion; and (ii) understanding the limitations of the available predictive models and the potential for their improvement.