  The hydrodynamic slippage at a solid-liquid interface is currently at the
center of our understanding of fluid mechanics. For hundreds of years this
science has relied upon no-slip boundary conditions at the solid-liquid
interface that has been applied successfully to model many macroscopic
experiments, and the state of this interface has played a minor role in
determining the flow. However, the problem is not that simple and has been
revisited recently. Due to the change in the properties of the interface, such
as wettability and roughness, this classical boundary condition could be
violated, leading to a hydrodynamic slip. In this chapter, we review recent
advances in the understanding and expectations for the hydrodynamic boundary
conditions in different situations, by focussing mostly on key papers from past
decade. We highlight mostly the impact of hydrophobicity, roughness, and
especially their combination on the flow properties. In particular, we show
that hydrophobic slippage can be dramatically affected by the presence of
roughness, by inducing novel hydrodynamic phenomena, such as giant interfacial
slip, superfluidity, mixing, and low hydrodynamic drag. Promising directions
for further research are also discussed.
