I applied online, contacted by a recruiter 1 - 2 weeks later to set up a phone interview.
Phone screening consisted of the recruiter outlining the position, me talking through my resume, and some casual conversation. Very relaxed, just be personable and know the position, your resume, and Southwest inside and out.
I was also contacted for the In-Flight Crew Scheduler opening. The phone interview was a similar format, but the second was much more personality driven - the recruiter had lots of energy and was obviously looking to tap into your personality as part of the screening. (I was not contacted to interview in-person for this position, I believe due to the forthcoming offer for the other opening)
I was contacted for an in-person interview for the Flight Ops Crew Scheduler position. They were flexible, I had to reschedule once due to my work schedule. I interviewed with the phone screening HR interviewer and the hiring manager. Similar format to the phone screening: walk me through your resume, what do you know about the position, why Southwest-type of questions. Also mixed in were some 'tell me about a time when...' questions, basically seeing how you would react in challenging situations related to the job. I must have interviewed with the same folks as the interviewee in the previous post, as the hiring manager was obviously very tired (eyes glazed, head-bob, just struggling), but knowing their schedule I gave him the benefit of the doubt and continued talking, focusing on the HR manager.
They gave me the opportunity to ask a few questions about the position (highly recommend good, thought-out questions, they seemed to appreciate the opportunity to talk more about the opening and company), which was engaging and also brought the hiring manger back to life, then the interview was over.
Overall a good impression, friendly folks and a great company from what I hear/read.