In the 1980s,Shechtman discovered quasicrystals with icosahedral symmetry in an Al-Mn alloy,a groundbreaking finding that shocked the scientific community and later earned him the 2011 Nobel Prize in Chemistry.The discovery of quasicrystals has redefined the framework for observing and classifying matter,expanding the understanding of crystal structures from the established 230 space groups to an infinite array of possibilities.Initially,quasicrystal research focused on metallic alloys,but as research progressed,scientists also identified quasicrystals in soft matter.These soft materials,which form unique supramolecular structures through self-assembly,have significantly enriched and advanced quasicrystal research.This paper provides a comprehensive review of various soft materials capable of forming quasicrystals,including dendrimers,block copolymers,surfactants,giant amphiphiles,and biomolecules.Soft matter quasicrystals have demonstrated considerable potential in diverse applications,such as drug delivery,sensor development,and energy storage.The study of quasicrystals in soft matter not only extends the fundamental theories of materials science but also offers new perspectives and potential breakthroughs in understanding material structures and their innovative applications.