I think most people who study this would say the common denominator is that metals lack a band gap and have a very mobile sea of electrons, and therefore good conductivity. Metals can be amorphous, or crystalline, or anywhere along the spectrum.
The "new school" certainly hasn't forgotten, or ignored, that crystals are patterns that tile all of space. These are known as space groups, and they enumerate every way to tile 3D space symmetrically (https://en.wikipedia.org/wiki/Space_group).
Anyways, I can guarantee that people who really study the subject absolutely take courses in metallurgy, crystallography, 3D math, and much more.
Also, if you're interested in simulations, I don't do that much myself, but you can always run some open source simulation software. http://www.opencalphad.com/