I did an over-the-phone interview (about 30 minutes) about a month after submitting a cover letter/resume/clips/critique of a Slate article. I didn't know anyone at the company, so it was a cold application. Later (about 1.5 weeks or so after the interview, so when I had begun to give up hope of getting the internship), I was asked to provide references, and shortly after my editor let me know he had been on the phone with Slate, I got the job offer over the phone.