I this talk, I will give semiorthogonal decompositions of derived categories of several classical moduli spaces, e.g. symmetric products of curves, Brill-Noether loci, (relative) Quot schemes, Hilbert schemes of points. In particular, they contain a proof of Jiang’s conjecture for semiorthogonal decompositions of Quot schemes of locally free quotients. They are by-products of my research on categorifications of wall-crossing in Donaldson-Thomas theory, and the proofs involve techniques of derived algebraic geometry, categorical Hall algebras, matrix factorizations and Koszul duality.