I applied online through Southwest's Career page on a Tuesday. A couple days later, on Thursday, I was emailed by a recruiter who wanted to set up a phone screen the following day (Friday). Did the phone screen. Just the recruiter going over my resume and skills. After the phone call, he said that based on our talk, they wanted to fly me out to their HQ for an in person interview.
I was called on the following Monday by another recruiter to set up flights and the interview. I flew out on that Thursday. The interview was an hour long. It was me, the initial recruiter, and 3 team members. They asked about my skills and what I was doing. And then went through a couple of development questions and scenarios.
All in all, it was a good experience. You can tell Southwest cares about setting up a good first impression.