Abstract: Wetting phenomena at "small" scales (a water drop on a glass, the precorneal tear-film) may be described by quite a few different mathematical models: diffuse interface ones, sharp ones such as the Navier-Stokes equations, and reduced ones such as the lubrication and the quasi-static approximations. Furthermore, they open up fundamental questions whose answer is yet debated, such as the description of the interface (if any) which separates "dry" from "wet" regions. Which model and which answer are most appropriate is likely to depend on the physics of the specific phenomena, and I will provide introductory information for most of them. However, all of these models are grounded on a basic and unifying physical mechanism: the balance of capillary and frictional (e.g. viscous) forces. Enlightening this principle will hopefully help understanding and enjoying the subsequent lectures within this series.