In this talk, we will consider a class of nonlocal viscous Cahn-Hilliard equations with Neumann boundary conditions for the chemical potential. The double-well potential will be allowed to be singular (e.g. of logarithmic type), while the singularity of the convolution kernel will not fall in any available existence theory under Neumann boundary conditions. We will prove well-posedness for the nonlocal equation in a suitable variational sense. Secondly, we will show that the solutions to the nonlocal equation converge to the corresponding solutions to the local equation, as the convolution kernels approximate a Dirac delta. The asymptotic behavior will be analyzed by means of monotone analysis and Gamma-convergence results, both when the limiting local Cahn-Hilliard equation is of viscous type and of pure type. This is based on a series of joint works with H. Ranetbauer, L. Scarpa, and L. Trussardi.