I just figured this out, under General Settings go to User Verification and select Admin Verification. This will send an alert email when a new application is filled out.
Also, the emails are all customizable, from what you get when an application is filled out to what they get, but make sure to edit the right ones and probably do a couple test applications.
Once a user has applied, you can go to Users -> Unverified Users to see who has applied and decide whether to approve them or not.