For vim there is a filesystem explorer called NERDtree: https://github.com/scrooloose/nerdtree
Surely an alternative or superior package exists for Emacs?
I prefer dirtree
(screenshot below) by Ye Wenbin. It feels pretty close to NERDTree / the TextMate drawer.
It took me a few minutes of trial and error to figure out the dependencies, so take a look at the install instructions (and a few minor edits to the source) I've got in this repo.