In this talk, we will consider a class of nonlocal Cahn-Hilliard equations both with Dirichlet and with Neumann boundary conditions for the chemical potential. After discussing local asymptotics in different settings, we will specify our analysis to a tumor growth model coupling a viscous Cahn-Hilliard equation describing the tumor proportion with a reaction-diffusion equation for the nutrient phase parameter. In particular, we will discuss first-order optimality conditions for suitable associated optimal control problems. This is based on a series of joint works with H. Ranetbauer, E. Rocca (Pavia), L. Scarpa (Milan), and L. Trussardi (Graz).