Constrained　submodular　maximization　(CSM)　is　widely　used　in　numerous　data　mining　and　machine　learning　applications　such　as　data　summarization,　network　monitoring,　exemplar-clustering,　and　nonparametric　learning.　The　CSM　can　be　described　as:　Given　a　ground　set,　a　specified　constraint,　and　a　submodular　set　function　defined　on　the　power　set　of　the　ground　set,　the　goal　is　to　select　a　subset　that　satisfies　the　constraint　such　that　the　function　value　is　maximized.　Generally,　the　CSM　is　NP-hard,　and　cardinality　constrained　submodular　maximization　is　well　researched.　The　greedy　algorithm　and　its　variants　have　good　performance　guarantees　for　constrained　submodular　maximization.　When　dealing　with　large　input　scenario,　it　is　usually　formulated　as　streaming　constrained　submodular　maximization　(SCSM),　and　the　classical　greedy　algorithm　is　usually　inapplicable.　The　streaming　model　uses　a　limited　memory　to　extract　a　small　fraction　of　items　at　any　given　point　of　time　such　that　the　specified　constraint　is　satisfied,　and　good　performance　guarantees　are　also　maintained.　In　this　chapter,　we　list　the　up-to-date　popular　algorithms　for　streaming　submodular　maximization　with　cardinality　constraint　and　its　variants,　and　summarize　some　problems　in　streaming　submodular　maximization　that　are　still　open.　©　2019,　Springer　Nature　Switzerland　AG.