With　the　progression　of　technology,　models　of　linear　multistate　consecutively-connected　systems　(LMCCSs)　have　been　applied　more　widely,　such　as　in　telecommunication　systems　and　the　Internet　of　Things,　among　other　applications.　LMCCSs　contain　a　series　of　linearly　arranged　nodes,　and　any　disconnection　between　nodes　will　lead　to　the　failure　of　the　entire　system.　Thus,　the　reliability　of　a　linear　multistate　system　is　affected　by　many　factors,　such　as　the　positioning　of　elements.　To　be　able　to　incorporate　different　types　of　complicated　practical　factors,　researchers　have　proposed　various　extensions　for　the　LMCCS　model.　Moreover,　models　have　been　proposed　to　study　the　optimal　system　configurations　of　such　systems　while　considering　reliability　and　some　other　objectives　or　constraints.　Due　to　the　amount　of　existing　research　on　LMCCSs,　this　paper　aims　to　review　the　related　literature,　classify　these　works,　and　elicit　some　future　research　directions.　©　2021　Bentham　Science　Publishers.