Proton　exchange　membrane　fuel　cells　(PEMFCs)　are　considered　to　be　an　important　low-carbon　energy　conversion　technology,　which　has　shown　impressive　performance　improvement　in　the　past　decades.　However,　the　sluggish　kinetics　of　the　oxygen　reduction　reaction　(ORR)　at　the　cathode　has　been　an　impediment　to　the　successful　commercialization　of　the　technology.　Novel　highly　active　electrocatalysts　for　the　ORR　are　highly　desired　to　meet　the　US　DOE　performance　targets.　In　recent　years,　polyhedron-engineered　Pt-alloy　nanocrystals　have　demonstrated　unprecedented　electrocatalytic　activity.　Different　from　previous　reviews　on　shape-manipulated　Pt-based　ORR　catalysts,　this　review　focuses　on　3D　polyhedron-engineered　Pt-based　nanocrystal　electrocatalysts　with　an　in-depth　comparison　of　different　active　facet-tailored　geometric　configurations　and　their　advanced　electrocatalytic　properties.　The　review　carefully　examines　and　criticizes　the　aggregated　data　in　this　area,　and　provides　an　important　overview　as　well　as　a　critical　insight　into　the　topic.　Understanding　the　catalytic　mechanism　taking　place　with　polyhedron-designed　Pt-based　nanocrystals　helps　to　unlock　the　door　to　highly　active　ORR　electrocatalysts　for　PEMFC　applications.