The fundamental underpinnings of a well-composed landscape shot takes into account three concepts: simplicity, flow and relationships.
 
Within those concepts, the landscape photographer explores space, lines, color theory, balance, how a viewer's eye moves through the shot, and how the different parts of a photo echo, contrast or expand upon each other.
 
Combine those ideas with lens choices, tripod heights and the ideas of how to approach a composition as a painting instead of a photo and you get Bryan's methods for landscape composition.