As　one　of　the　most　classical　data-storage　systems,　magnetic　recording　(MR)　systems　have　attracted　a　significant　amount　of　research　attention　in　the　past　several　decades　due　to　the　advantages　of　low　cost　and　high　storage　density.　Along　with　the　continual　increase　of　areal　density　of　modern　MR　devices,　more　severe　inter-symbol　interference　(ISI)　and　noise　appear　and　thus　reliable　storage　becomes　more　difficult.　To　address　this　challenging　problem,　turbo　detections　and　error-correction　codes　(ECCs)　have　been　applied　to　MR　systems　so　as　to　significantly　improve　the　overall　data-storage　reliability.　Among　all　the　existing　ECCs,　low-density　parity-check　(LDPC)　codes　are　of　particular　interest　because　they　can　offer　excellent　error　performance　with　relatively　low　encoding　and　decoding　complexity.　This　paper　presents　a　comprehensive　survey　of　the　latest　research　advancements　in　LDPC-code　design　for　MR　systems　from　the　perspectives　of　code　construction,　decoder　design,　as　well　as　asymptotic　performance-evaluation　methodology.　More　specifically,　we　summarize　the　design　guidelines　of　LDPC　encoder　and　decoder　over　both　one-dimensional　(OD)　ISI　and　two-dimensional　(TD)　ISI　channels,　which　are　commonly　used　to　characterize　MR　systems　with　different　areal　densities.　We　also　concisely　portray　the　research　progress　in　the　design　of　some　LDPC-code　variants,　such　as　protograph　codes,　repeat-accumulate　codes,　spatially　coupled　codes,　and　their　non-binary　counterparts　over　the　aforementioned　ISI　channels.　In　particular,　we　restrict　our　attention　to　the　reading　process　and　ignore　the　written-in　errors　in　MR　systems　unless　otherwise　stated.　Hopefully,　this　survey　will　inspire　more　research　activities　in　the　area　of　LDPC-coded　MR　systems.　©　2018　IEEE.