I applied with a cover letter and CV, and received an email two weeks later inviting me for an interview the following week. After the brief phone call (ca. 30 minutes) I only heard back from them a month later, when I was informed they had hired another person.
I applied through an employee referral. The process took 4 weeks. I interviewed at Sotheby's (Milan) in Feb 2020
Interview
The interview is divided in two phases. In the first one, they would ask you info about your previous career and academic background. Then routine questions on the reasons why you applied, plus why you should get the job.
The second phase consists of recognition and analysis of different works of art, depending on the department you are applying for.
Interview questions [1]
Question 1
Why Sotheby's? What your previous experience could make you a good candidate?