Most schools have secondaries... So, that will be their way of notifying you. They will send an email that says "we've received your app. Here is the secondary for you to complete. give us your moneyyyyyz!"
Fewer schools will update you with the review process. Off the of my head, I remember Western, Case Western, and Iowa being REALLLLLLY good about keeping you updated. The rest of the schools all kind of just ignore you until they offer an interview or reject you.
The only sign of a school's office actually working with my app was the "application received" email and my check being cashed. haha!