I will discuss the use of a diffuse-interface model for simulating moving contact lines. The Cahn-Hilliard diffusion is known to regularize the singularity and makes possible a continuum-level computation. But relating the results to physical reality is subtle. I will show numerical results that suggest a well-defined sharp-interface limit, with a finite contact line speed that can be related to measurements. Furthermore, I will discuss applications of this model to simulate enhanced slip on textured substrates due to contact line depinning, with viscous or viscoelastic liquids.