The first interview was with a recruiter. I met up with them, and it was a conversation so they could get to know me, they asked me about myself, why I picked the New York Times, if I was comfortable working alone, etc. They also let me know which team was interested in working with me. Then she asked me if I had any questions. A week later, I got an email for a second interview. The second interview was with one senior product designer and one lead product designer. They send you an email beforehand in which they inform you about the structure of the interview (present a project of yours for 10 mins and 20 mins for questions and conversation). I presented a project for around 12 minutes. In the email, they said they'd be asking questions during the presentation, but they stayed silent until the end, when they asked me a couple questions. They seemed pretty satisfied. Then, we moved on to behavioral questions. They explained a bit about the projects they worked on in their team, and then they asked me several questions about teamwork, collaboration, and dealing with conflict. We'd reached the 30 minute mark and were wrapping up, but then one of the designers asked me one last question, which I think he thought of on the spot. Three weeks later, the recruiter who'd originally gotten in touch with me emailed me with an offer.

initial phone call first round/behaviorial, second round video interview with portfolio review for the second round, both 30 minutes, personally had no referral and cold applied. did not get the offer for the internship at the end.