You may be surprised, but one doesn't even need explorer. Shell works in this matter quite fine, especially if one uses many relatively short-lived Vim sessions (as opposed to one huge session for all the editing tasks within the project).
CtrlP [1] with its fuzzy search is really a delightful way to move around projects with many files. If you have an extraordinary amount of files you can also add ag [2] in the mix [3] for faster searching/grepping.