Is it appreciated to contact old phd advisors with updates on what you have been doing?

I always appreciate such messages from old students. I often wonder what they are getting up to. I don't think I'm unique in that, but some would, perhaps, not be as happy with "interruptions." But you will get a sense of whether you should continue it if you do this from the response.

Going back in person is also a nice thing to do if you get the opportunity. Not only for advisors, but also for old mentors that you think had a positive impact on your life and career.

If it annoys them, you will hear about it, or they will just ignore you. But I think it is a professional courtesy to keep people updated. Many of them have invested something in you and like to hear how the investment has turned out.

I expect there are some supervisors that would be annoyed by this, but I suspect they would be in the minority. A supervisor invests a lot into a student, and unless you left on bad terms, its most likely they'd love to hear how you are doing, I know I would.

About 10 years after getting my Masters in CS I came across an obscure feature on a software project I was doing on the side. It involved discrete math, which is mostly theoretical. Dr Itoga had taught this at the University of Hawaii, my alma mater.

I decided to send him an email telling him that I finally had a chance to use what he had taught me, and that he should his students that you never know what CS skills you are going to use in industry.

The next day I get an email reply that he always hearing from his former students, and asks if he can post what I said for his students.

Of course I replied yes. I told this story to a friend, who then tracked down Dr Itoga's post to his students with my words quoted.

Although it will depend on your relationship with your advisor or professor, in general, yes, they appreciate you reaching out.