I went to the JHU APL booth at a career fair. They took my information and also told me to apply online. I heard back from them several weeks later offering me an on-site interview. They paid for me to spend the night in Columbia, MD.
The next morning, I met with the HR department first and went over some of the benefits (which are great by the way). This was a very easy enjoyable non-threatening conversation which got me warmed up for the 1-on-1 meetings later throughout the day. Next, I met with my would-be immediate supervisor, who was incredibly friendly. We discussed what kind of work they perform. I was asked some of the typical personality questions (i.e. leadership, weaknesses, strengths). Next, I met with various people within the group to get some different perspectives from people who had been there for a while versus people who had joined the group within the year. This was a great opportunity to really get some honest opinions about working with the group and the type of work the perform. I had lunch with some of the newer members. Then, they allowed me to tour one of the group's labs to show me some of the non-confidential work.
About 1.5 months later, I was extended an offer. I had interviewed several places and had a few other offers on the table. JHU APL was incredibly patient with me as I finished my tour of interviews (a couple months). I spoke with my would-be immediate supervisor multiple times via email and phone about some questions I had. I even received a call from his supervisor asking if I had any questions or if they could help me in any way. They were incredibly open, honest, and friendly (especially my would-be immediate supervisor) about why they wanted me, and why I would be a good fit. They even provided me with a bulleted list of why they wanted me so badly. They were also NOT pushy in any way, saying that they completely understood that I needed to make the best career choice for me and my family. I couldn't have imagined a better interaction. I was completely floored by how nicely they handled the situation. It was miles better than my post-offer interactions with the other 3 companies I had offers from. After I accepted the offer, I got the nicest email from my immediate supervisor indicating how excited he was that I accepted and how he was looking forward to me starting.