Bit-interleaved　coded　modulation　(BICM)　has　attracted　considerable　attention　from　the　research　community　in　the　past　three　decades,　because　it　can　achieve　desirable　error　performance　with　relatively　low　implementation　complexity　for　a　large　number　of　communication　and　storage　systems.　By　exploiting　the　iterative　demapping　and　decoding　(ID),　the　BICM　is　able　to　approach　capacity　limits　of　coded　modulation　over　various　channels.　In　recent　years,　protograph　low-density　parity-check　(PLDPC)　codes　and　their　spatially-coupled　(SC)　variants　have　emerged　to　be　a　pragmatic　forward-error-correction　(FEC)　solution　for　BICM　systems　due　to　their　tremendous　error-correction　capability　and　simple　structures,　and　found　widespread　applications　such　as　deep-space　communication,　satellite　communication,　wireless　communication,　optical　communication,　and　data　storage.　This　article　offers　a　comprehensive　survey　on　the　state-of-the-art　development　of　PLDPC-BICM　and　its　innovative　SC　variants　over　a　variety　of　channel　models,　e.g.,　additive　white　Gaussian　noise　(AWGN)　channels,　fading　channels,　Poisson　pulse　position　modulation　(PPM)　channels,　and　flash-memory　channels.　Of　particular　interest　is　code　construction,　constellation　shaping,　as　well　as　bit-mapper　design,　where　the　receiver　is　formulated　as　a　serially-concatenated　decoding　framework　consisting　of　a　soft-decision　demapper　and　a　belief-propagation　decoder.　Finally,　several　promising　research　directions　are　discussed,　which　have　not　been　adequately　addressed　in　the　current　literature.　©　2022