Acoustic　metastructures　(AMs)　are　a　type　of　artificial　engineering　materials　composed　of　various　micro-meso　structure　subwavelength　units.　They　can　exhibit　distinct　and　exotic　performances　such　as　low　mass,　low　volume,　low　frequency,　and　broadband　through　appropriate　structural　designs,　which　provide　novel　means　for　the　exploration　of　physical　interpretation　in　terms　of　individual　case.　Thus,　the　design　strategies　of　AMs　for　unprecedented　properties　are　of　growing　interest　and　attention.　Beginning　with　the　recent　advances　in　structural　design,　a　comprehensive　review　of　the　physical　mechanisms　and　structural　characteristics　of　four　typical　AMs,　i.e.,　Helmholtz　resonators,　membrane-type　AMs,　coiling-up　space　structures,　and　lattice　structures,　is　performed.　Meanwhile,　various　engineering　application　potentials　associated　with　regard　to　performance　evolutions　including　sound　absorption　and　noise　reduction,　acoustic　cloaking,　and　acoustic　lenses　are　introduced,　as　well　as　the　corresponding　design　optimization　strategies.　Finally,　the　current　scientific　and　technical　challenges　and　the　developmental　trends　of　AMs　are　summarized.　This　review　work　aims　to　provide　a　design　roadmap　for　next-generation　AMs　and　a　trigger　on　unsuspected　physical　mechanisms.