The non-Hermitian skin effect has been theoretically predicted then experimentally observed in one dimension. This effect has twofold meanings: the eigenvalues of a non-Hermitian band differ drastically under periodic boundary and open boundary conditions; and the eigenstates of a non-Hermitian band under open boundary condition differ drastically from the Bloch states. In this talk, I will first review several key results on the skin effect in one dimension, including its qualitative relation to the spectral winding number, which is a topological invariant unique to non-Hermitian bands. I will then show some new results in 2D and higher dimensions that demonstrate the universal presence of the skin effect. Here “universal” means that (i) it does not need any symmetry for its protection, unlike topological edge modes; and (ii) it is compatible with all spatial symmetries, unlike its 1D counterpart. A natural consequence of this universality is the prediction that any non-Hermitian band having nontrivial exceptional points must also show skin effect, which has recently been observed in an experiment.