Static and Dynamic Maps and Borders

Maps and borders are strange things.  We are acquainted with them relatively early in life and they serve as a useful way for us to adopt a more abstract view of the world around us.  In strategy and war games, the vast majority of our time is spent staring at a map.  How the map is designed then, becomes a crucial component of the player's experience, as it literally determines how we play, and think about, the game.  I think to describe a strategy game's map design we should answer two (slightly unrelated) questions:

1. How are borders and territories drawn?
2. How do players move their forces around?