The protection of buildings and structures against blast loads has long been of significance and attracted continued attention of research and industrial communities. Rather than strengthening the structures themselves, possible application of attaching cellular materials and structures to the exterior of structures to alleviate load on them is reviewed. First the properties of cellular solids under typical loading conditions, i.e., quasi-static compression, low to mediate rate compression, as well as high velocity compression, are briefed. Then the dynamic behavior of the composite structures containing cellular materials subjected to blast loads is introduced. The emphasis is placed on the dynamic response of blast mitigation cladding and their protection efficiency. Amongst, the analysis methods in terms of energy absorption and impulse transfer are surveyed and the fundamental problem of whether attaching cladding with cellular solid core to the exterior of protected structure can effectively mitigate blast load is discussed. Throughout the review, merits and drawbacks of the existing models and applications are examined and discussed. Some possible future directions on structure blast mitigation with cellular solid cladding are presented, inclusive of blast mitigation cladding with gradient cellular solid cores of specific density variations, active protection cladding rather than the traditionally studied passive protection methods.