There is a least one thread about cancellations in general (How Are Your Refunds Going?), but I thought it might be helpful to start one that was more specific to one airline. (The thread mentioned had several descriptions of how things went with Delta, and they were mostly positive.)
First, let me say I like Delta. I think they have done a better job than many other airlines during the pandemic (and a better job generally before the pandemic).
I have run into one glitch, however, that bears a caution to others. The caution first: Do not try to cancel a flight online or through the app as Delta asks you to. I explain why below.
I had to cancel a domestic flight that was scheduled for late March and an international flight scheduled for late April. I did the domestic one first, but the online system actually would not complete the cancellation. This attempt was early in March as things were shutting down so I then tried calling, but really could not get through due to the wait times. Totally understandable. I tried sending a direct message through Twitter -- I have a Twitter account solely for this sort of thing -- and I got a response fairly quickly. I explained my situation and the reservation was cancelled and I got a full refund credited to my account within a few days.
I waited until later to try and cancel the international flight, as Delta asked its customers to wait until closer to the date of the flight. I tried to do so online again for two reasons: 1) Delta asked me to in its recorded messages and posts on its web site, and 2) I thought five or six weeks later that the system would work.
On this effort, it looked like my attempt would work. I got to a later screen that showed the amount of the full refund. When I hit the "submit" button, I got an error message that said the cancellation would not go through and that I would have to contact Delta. But then, almost simultaneously, I got an email confirming the cancellation and the $350 cancellation fee. Say what? The cancellation fee did not show on my screen when I hit "submit." In fact, it never showed.
I had been getting emails from Delta and seen public notices from the airline that stated that any cancellation fees had been waived for flights cancelled due to the virus. My cancellation was not a whim, either: The country I had a ticket to travel to had closed its borders to visitors from the U.S. and Delta had changed my flight (or actually, flights) so that one leg of the flight was scheduled to arrive after the next leg was scheduled to depart. That is, Delta had rescheduled my trip with a flight it was impossible for me to make.
Delta credited my account for the amount of my ticket within a few days, but less the $350 cancellation fee. I have been in contact with Delta three times since this took place to find out if I can expect this fee to be credited back to me. Unsuccessful so far, and I can tell by the signs that my refund request has dropped into a black hole in Delta's computer system. In my third contact, the CSR admitted that I should not have been charged the fee and that it resulted from the automated system. I suspect I will need to have more communications with Delta about this before there is any resolution. Hence my caution: Do not attempt any automated cancellation. Go through the steps to speak or communicate with a human person.