There has been a lot written about Canonical's interview process, and unfortunately most of it is negative. It certainly has its quirks, as I will describe below, but in general the process was smooth and efficient and I enjoyed going through it.
The stage that gave me the most trouble was the "written interview", which involves answering 30+ questions about the company, your career, your experience with open source and perhaps infamously, your high school grades and achievements. This is also the first thing that you have to do after the initial application!
It can take a long time to fill out, but you are given two weeks to do it which should be plenty of time if you do a little every day - just don't be like me and write 95% of it in the last two days, causing yourself a great deal of avoidable stress.
There's also the Thomas General Intelligence Assessment (GIA) to complete, a lot of interviews (6-10, depending on the position) and a personality test, but you can deal with those later. The GIA can and should be practiced with the free examples available on the internet, and interviews are simply a matter of preparation.
Don't forget to go over your written interview so that you can respond to any follow-up questions that may come up - again, don't be like me and get flustered by an interviewer asking you to clarify an answer that you've completely forgotten in the intervening weeks/months since submission!
Once past the written interview and the Thomas GIA, the interviews were straightforward, albeit more numerous than I've experienced in the past. I enjoyed talking to people from different teams and regions, and had no real issues with the process apart from its length.
A shorter process would have been nice, but Canonical have been very explicit about their reasons for the process being what it is, and you'll have a much better time of it if you just accept what it is and just go with the flow.
If you are thinking of applying, I highly recommend reading this blog post as it helps explain some key points about the process and how you should prepare to give yourself the best chance of success. May the odds ever be in your favour.
https://canonical.com/blog/how-to-get-a-job-at-canonical