Cellular　media　materials　are　used　for　automobiles,　aircrafts,　energy-efficient　buildings,　transportation,　and　other　fields　due　to　their　light　weight,　designability,　and　good　impact　resistance.　To　devise　a　buffer　structure　reasonably　and　avoid　resource　and　economic　loss,　it　is　necessary　to　completely　comprehend　the　constitutive　relationship　of　the　buffer　structure.　This　paper　introduces　the　progress　on　research　of　the　mechanical　properties　characterization,　constitutive　equations,　and　numerical　simulation　of　porous　structures.　Currently,　various　methods　can　be　used　to　construct　cellular　media　mechanical　models　including　simplified　phenomenological　constitutive　models,　homogenization　algorithm　models,　single　cell　models,　and　multi-cell　models.　This　paper　reviews　current　key　mechanical　models　for　cellular　media,　attempting　to　track　their　evolution　from　their　inception　to　their　latest　development.　These　models　are　categorized　in　terms　of　their　mechanical　modeling　methods.　This　paper　focuses　on　the　importance　of　constitutive　relationships　and　microstructure　models　in　studying　mechanical　properties　and　optimizing　structural　design.　The　key　issues　concerning　this　topic　and　future　directions　for　research　are　also　discussed.