The moving contact line problem is a classical problem in
fluid mechanics. The difficulty stems from the fact that the classical
continuum theory with no-slip boundary condition predicts a non-physical
singularity at the contact line with infinite rate of energy
dissipation. Many modified continuum models are then proposed to
overcome this difficulty.
They all succeed in removing the singularity, but they leave behind the
question: which one of these models is a good description of the
microscopic physics near the contact line region? We will review the
results obtained using continuum theory, molecular dynamics and the more
recent multiscale techniques. We will also discuss how these techniques
can be combined to give us a better understanding of the fundamental
physics of the moving contact line and formulate simple and effective
models.