Yes, but you have to be on v3 of the website. The link is on the Tournaments page.
View Previous live tournaments

Well, v3 is still in progress and is essentially in beta, so there may be some missing features and bugs. For the latter there is a way to report via the interface, and you should if you run across any.
The link to switch is at the bottom of most pages, listed as Try the new Chess.com

Yeah, I think staff mainly wants really interested people to test. Not too long ago it was only open to premium members that were part of the v3 group. It is now available to everyone but not widely publicized, mainly I think to not overload staff
I do almost everything on v3, though I'll occasionally have to switch back if I encounter issues.
Is there any way to view previous live tournaments you participated in? I would like to review them, but after the tournament was over all the information about standings, pairings, etc. disappaeared. Is there any place to find this?