Applied through employee referral and filled out my profile online. Was contacted by HR Manager to set up a phone interview discussing background, the role itself, salary, etc. If that is up to par or in line with what they are looking for, the HR Manager will send your resume forward to the team members who are in charge of the interviewing and hiring (typically managers and senior managers).
I was checking my status through the online portal throughout the process and about a week after my phone interview my status had changed to "interview requested". The HR contact I've been dealing with called to schedule a time to come into the office and interview with the team.
I knew they were trying to fill the position quickly and it helped to have multiple contacts within the company, so they let me know that it should be quick turnaround in the decision making and I heard their decision 2 days after my in-office interview. The longest part of the process is usually between initial application - phone interview - in-office interview. After that, they are quick in letting you know their decision.