Why is surface tension a force parallel to the interface?

A paperclip can float on water. Drops of mercury do not spread on a surface. These capillary phenomena are macroscopic manifestations of molecular interactions and can be explained in terms of surface tension. We address several conceptual questions that are often encountered when teaching capillarity and provide a perspective that reconciles the macroscopic viewpoints from thermodynamics and fluid mechanics and the microscopic perspective from statistical physics.