Sketching and streaming algorithms are in the forefront of current research directions for cut problems in graphs. In the streaming model, we show that $(1-ε)$-approximation for Max-Cut must use $n^{1-O(ε)}$ space; moreover, beating $4/5$-approximation requires polynomial space. For the sketching model, we show that $r$-uniform hypergraphs admit a $(1+ε)$-cut-sparsifier (i.e., a weighted subhypergraph that approximately preserves all the cuts) with $O(ε^{-2} n (r+\log n))$ edges. We also make first steps towards sketching general CSPs (Constraint Satisfaction Problems).