In　the　past　two　decades,　chaotic　modulations　have　drawn　a　great　deal　of　attention　in　low-power　and　low-complexity　wireless　communication　applications　due　to　their　excellent　anti-fading　and　anti-intercept　capabilities.　Of　particular　interest　is　the　differential　chaos　shift　keying　(DCSK),　which　is　considered　as　a　very　promising　chaotic　modulation　scheme　that　achieves　not　only　good　error　performance,　but　also　low　implementation　complexity.　In　this　treatise,　we　provide　an　insightful　survey　on　the　state-of-the-art　research　in　DCSK-based　communication　systems　through　an　extensive　open　literature　search.　In　doing　so,　we　firstly　review　the　principles　of　DCSK　modulation　and　the　significant　milestones　since　its　inception.　Subsequently,　we　introduce　meritorious　variants　of　DCSK,　all　of　which　can　outperform　the　original　one　in　certain　aspects.　We　also　present　the　joint　design　guidelines　when　combining　DCSK　with　other　critical　techniques,　e.g.,　error-correction　coding　and　cooperative　communication,　in　wireless　communications　under　both　single-user　and　multiaccess　scenarios.　Besides,　we　summarize　research　progress　in　the　application　of　DCSK-based　communication　systems　to　ultra-wideband　scenarios　and　their　corresponding　advantages.　Specifically,　we　restrict　our　attention　to　the　relevant　modulation　and　system　designs,　as　well　as　their　performance-analysis　methodologies.　This　survey　aims　not　only　to　allow　researchers　understanding　the　development　and　current　status　of　DCSK-based　communication　systems,　but　also　to　inspire　further　research　in　this　area.