Elliptic and parabolic equations with rough coefficients in Sobolev spaces

We discuss some recent results on elliptic and parabolic equations (local and non-local, in divergence form and non-divergence form) in Sobolev spaces, especially when the coefficients are very rough. We also discuss a few approaches for the unique solvability of equations in Sobolev spaces. Some examples and counterexamples are presented to illustrate the advantages of having rough coefficients and the necessity of minor regularity conditions on the coefficients.