Photodetectors　(PDs)　have　great　potential　in　applications　of　imaging,　telecommunication,　and　biological　sensing.　In　this　article,　state-of-the-art　achievements　on　typical　low-dimensional　nanostructured　PDs　and　hybrid　PDs　are　reviewed.　In　the　2D　nanostructured　PDs　part,　2D　transition　metal　dichalcogenides　have　a　natural　gap,　which　promise　high　sensitivity　of　photodetection.　Graphene　and　black　phosphorus　can　also　stand　for　2D　nanostructured　PDs　due　to　their　broadband　absorption　and　tunable　direct　bandgap,　respectively.　In　the　1D　nanostructured　PDs　part,　owing　to　its　high　photoconductive　characteristic,　ZnO　nanowire　film　is　a　promising　material　for　ultraviolet　PDs.　Carbon　nanotubes　show　potential　in　infrared　(IR)　detection　due　to　its　unique　physical　properties.　In　the　0D　nanostructured　PDs　part,　lead　sulfide　has　a　small　bandgap　and　large　Bohr　exciton　radius,　which　collectively　give　it　a　wide　spectral　tunability　in　the　IR.　In　the　hybrid　PDs　part,　electrical　and　chemical　doping　is　applied　to　combine　different　nanomaterials　to　realize　PDs　with　high　performance.　In　each　part,　the　present　situation　and　major　challenges　are　overviewed.　Then,　the　evolutions　of　the　methods　to　overcome　these　challenges　and　the　tremendous　research　breakthroughs　are　demonstrated.　At　last,　future　directions　that　could　improve　the　performance　of　PDs　are　discussed.