In　this　paper,　we　shall　survey　some　connections　between　the　theory　of　set-valued　random　variables　and　Choquet　theory.　We　shall　focus　on　investigating　some　results　of　the　relationships　between　the　distributions　of　set-valued　random　variables　and　capacities,　and　also　some　connections　between　the　Aumann　integral　and　the　Choquet　integral.　Then　we　shall　review　some　results　on　laws　of　large　numbers　(LLN＇s)　for　set-valued　random　variables　and　for　capacities,　and　point　out　some　relations　between　these　two　kinds　of　LLN＇s.　Finally　we　shall　give　a　new　strong　LLN　of　exchangeable　random　variables　for　capacities.