Paper applications are primarily a thing of the past. From the HR side, online applications give a wider pool of candidates (not just those who walk in, but those who find us online) and the application software makes it easy for HR professionals to sort and review applications and resumes.
The reality is that the majority of people who apply for a position will not receive a phone call (but if you do, please check your voicemail). That being said, you need to check your email frequently when you are in the job search. Many programs will send an automatic response that you application has been received. This doesn't mean that a real person has actually looked at your application or resume, but that it has been received by the system. It's probably also a good idea to check your spam or junk folder as these responses may be filtered by your friendly email provider.
You may be asked to take some kind of survey or assessment as a part of the application process. This will also come through email. If you rock the interview and the company likes you and wants to move forward with you, they may send you new hire paperwork, background consents or electronic I9's that need to be completed.
Sadly, disappointment also comes via email. If you don't meet certain criteria simply based on your application (ie you request $100k per year for a position that pays $12/hour), you will get a "Thank you for your interest" email. If you interview but another candidate is selected, you may get a "Thank you for interviewing" email.
The bottom line? Phone calls are few. Please check your email.