Continuum　robot　has　good　motion　flexibility　and　strong　environmental　compliance.　It　can　well　adapt　to　large　deformation　and　complex　environment,　and　can　carry　out　safe,　dexterous　and　accurate　intelligent　interaction　between　robot　and　environment.　Because　of　the　above　advantages,　continuum　robot　can　be　widely　used　in　medical　equipment,　industrial　production　and　other　fields.　The　realization　of　safe,　stable　and　flexible　intelligent　interactive　operation　of　continuum　robot　in　constrained　space　is　the　focus　and　difficulty　in　these　fields.　The　research　status　of　continuum　robot　system　is　investigated　and　analyzed　in　aspects　of　model　analysis,　trajectory　planning　and　control　methods　in　this　manuscript,　so　as　to　provide　a　useful　reference　for　scholars　related　to　continuum　robot.　©　2024　IEEE.