This　article　aims　to　investigate　the　research　achievements　related　to　aerial　robots　with　physical　interaction.　Various　morphologies　of　aerial　physical　interaction　(APhI)　robot　prototypes　with　fixed　wing,　flapping　wing,　single　main　rotor,　conventional　underactuated　multirotor,　fully　actuated　multirotor,　even　deformed　multirotor,　and　multiple　platforms　are　reviewed　for　different　APhI　tasks　associated　with　momentary,　loose,　and　strong　interaction　coupling.　This　review　also　covers　APhI　robot　rigid　dynamics　and　robot-environment　coupled　interaction　dynamics　modeling　methods,　interaction　wrench　measurement/estimation,　decoupled　and　coupled　control,　active　aerial　interaction　control,　and　task-constrained　planning　approaches.　Finally,　future　development　directions　and　prospects　are　initially　anticipated　for　aerial　robots　with　physical　interaction.　Note　to　Practitioners-Aerial　physical　interaction　(APhI)　has　been　a　hot　topic　in　the　field　of　aerial　robots　in　recent　years,　which　is　a　reflection　of　the　advanced　capabilities　of　aerial　robots.　However,　APhI　robots　face　challenges　such　as　difficulty　in　flight　stability　and　weak　adaptability　to　dynamic　environments　while　exerting　active　influence　on　environments.　Under　this　background,　this　review　aims　to　offer　a　reference　for　researchers　and　practitioners　engaged　in　the　related　field　from　the　aspects　of　system　design,　modeling,　control,　and　task-constrained　planning,　which　hopes　to　help　them　apply　APhI　robots　to　polar　scientific　expeditions,　complex　environment　sampling,　infrastructure　inspection　and　maintenance,　and　other　application　areas.　Further,　this　review　also　highlights　the　design　idea　of　rigid-soft　integrated　APhI　robots　from　the　perspective　of　design-mechanism-performance　to　enhance　interaction　stability　and　safety.