The study of the morphology of surfaces produced by vapor deposition began over 125 years ago with Lord Kelvin. Since then, many researchers have addressed this topic from very different theoretical viewpoints, including thermodynamics, kinetics, fractal geometry, and numerical simulations. Only recently, however, have scanning probe microscopes become available to measure the three dimensional topography of a deposited film, which provided the quantitative experimental data necessary to test the different models of film growth. The concept of scaling provides a good first description of the morphology of vapor deposited films of all types, but for heteroepitaxial films, scaling is only approximately valid. The competition between the surface roughening caused by island nucleation and growth versus the smoothening actions of surface diffusion and desorption can lead to the formation of correlated structures on a surface with a dominant spatial frequency. By rational control of the film growth conditions, one can produce a surface covered by a low density of nearly monodisperse nanoparticles, an essentially fractal surface, or a planar film surface.