I applied through an employee referral. The process took 3 weeks. I interviewed at Etsy (New York, NY) in Jan 2017
Interview
It consists of three steps. The first phone screen is a call from a data scientist to discuss my past projects and my interests in Etsy. The second phone screen is a machine learning basic skill test. During 45 minutes, you get many questions that are similar to "speed quiz" with many "explain this concept". Make sure to review basic machine learning materials. Once you pass this, you are invited for an on-site interview. I heard that you'd be talking to 2-3 data scientists, and give 30-45 minutes of tech talk on your research, and of course the tour of their HQ! I withdrew at this step for another offer, but my overall experience about Etsy was awesome. The data scientists and the recruiters I've interacted are all nice and helpful.
The interview process consisted of three phone screens and an on-site portion that involved a 45 minute "job talk" and 3 more interviews. I ended up getting an internship offer for the summer, but I unfortunately had to decline. However, everyone I interacted with (from the team I would've been on to the recruiter) was extremely helpful and accommodating. I have nothing but positive things to say about Etsy! :-)