What's new for Themes in Ghost 0.4?

With the release of Ghost 0.4.1 yesterday, I wanted to take the time to finish this long put-off post detailing what has changed in the world of Ghost themes since 0.3.3. Yesterday's release included an upgrade to handlebars 1.3.0, so I'll cover highlights of what's new there as well.

This is a companion discussion topic for the original entry at https://dev.ghost.org/ghost-0-4-themes/