The　space　industry　in　China　is　eager　to　have　the　advanced　technology　of　large　space　structures　composed　of　trusses　cables　and　meshes.　Such　a　large　space　structure,　deployed　on　orbit,　may　serve　as　the　large　antenna　for　different　space　missions.　The　important　scientific　basis　of　the　technology　is　the　nonlinear　dynamics　modeling,　analysis　and　control　of　these　space　structures　during　their　deployment　and　service.　This　review　article　surveys　the　advances　in　relevant　researches　and　proposes　three　open　problems　as　follows.　The　first　is　the　flexible　multibody　dynamics　for　the　deployment　of　such　a　space　structure,　especially　the　nonlinear　dynamics　modeling　and　analysis　for　the　contacts　and　wraps　of　mesh　under　microgravity,　the　internal　impacts　in　clearance　joints,　and　the　coupling　between　structure　deployment　and　spacecraft　attitude.　The　second　is　the　dynamics　analysis　of　the　space　structures　after　deployment　and　during　service,　especially　the　complicated　nonlinear　vibrations　of　the　flexible　structure　with　numerous　backlash　joints　under　periodic　thermal　impacts.　The　third　is　the　dynamic　control　of　the　space　structures　after　deployment　and　during　service,　especially　the　under-actuated　and　lower-powered　control　for　structure　vibrations　and　waves.