Image　reconstruction　in　magnetic　resonance　imaging　(MRI)　and　computed　tomography　(CT)　is　a　mathematical　process　that　generates　images　at　many　different　angles　around　the　patient.　Image　reconstruction　has　a　fundamental　impact　on　image　quality.　In　recent　years,　the　literature　has　focused　on　deep　learning　and　its　applications　in　medical　imaging,　particularly　image　reconstruction.　Due　to　the　performance　of　deep　learning　models　in　a　wide　variety　of　vision　applications,　a　considerable　amount　of　work　has　recently　been　carried　out　using　image　reconstruction　in　medical　images.　MRI　and　CT　appear　as　the　ultimate　scientifically　appropriate　imaging　mode　for　identifying　and　diagnosing　different　diseases　in　this　ascension　age　of　technology.　This　study　demonstrates　a　number　of　deep　learning　image　reconstruction　approaches　and　a　comprehensive　review　of　the　most　widely　used　different　databases.　We　also　give　the　challenges　and　promising　future　directions　for　medical　image　reconstruction.