The problem

One problem to solve when doing web authentication has always been one identity provider, so you don't have to remember which username (or email address) you used for that bugtracker you used three years ago or that website. And tie it to one login ideally. Five years ago this problem seemed to be basically solved. There was OpenID and while it may not have been great it worked. You could have your own provider, your institution (university, company, foss project, ..) could have one and you could use your university-provided ID for all university stuff.

Today's state

Looking at the problem again today and the situation seems to have changed. To the worse. A lot. People are actively removing OpenID support. There seemed to be a replacement with, at least, proper design goals: Mozilla's persona. However this seems to be a dead end, no-one (almost) actually supports it.

Then there is what people call OAuth2. However there does not seem to be such a thing as OAuth2 at all, at least not for logging into websites. So for example phabricator supports 12 different OAuth2 systems. That includes Google, Facebook, Twitter, Amazon Github and a whole bunch of other services. Each with a different implementation in the webapp of course. And of course you can not just have your university/company/.. provide an OAuth2 service for you to use -- you would need to write yet another adapter on the (foreign) website to talk to your implementation and your provider.

And the strange thing, people seem to still consider OAuth2 a replacement for OpenID while it does not even provide the core functionality of the older system. Plus there does not seem to be any awareness of that all together.

Other features

Now of course, OpenID is not (and never was) the ultimate answer to the web authentication problem. The most obvious problem being user tracking. Your identity provider will see every website you log into, will see when you log into it and even be able to log into that website with your credentials.

Of course, this problem is fully inherited by OAuth2. And in contrast to OpenID you can no longer run your own provider whom you can fully trust and who already knows about your surfing habits (because it's actually you already). Mozilla's persona might have solved that, they at least intended to. But, again, persona seems quite dead.