Nonlocal evolution equations have been around for a long time, but in recent years there have been some nice new developments. The presence of nonlocal terms might originate from modeling physical, biological or social phenomena (incompressibility, Ekman pumping, chemotaxis, micro-micro interactions in complex fluids, collective behavior in social aggregation) or simply from inverting local operators in the analysis of systems of PDE. I will brifly present some regularity results for hydrodynamic models with singular constitutive laws. The main part of the talk will present a nonlinear maximum principle for linear nonlocal dissipative operators and applications.