In the event you deploy some code, a DB migration, a server configuration change, etc, and your solution fails after the fact, you move forward, not backwards. Let me explain further.
If you deploy v1.0 of your application and it works, great! If you then deploy v1.1 and it falls over, you find out why, apply a fix, test it locally (Vagrant?), deploy it to a testing environment and perform automated tests (Selenium, jMeter, ...), and once it's working there, you deploy it to production. This is called a hot fix, and it will now be working as intended (unless something else is horribly off the mark in which case you have other issues.)
The key to this example is the local and remote/network-based testing environment(s.) In my opinion, it's very much a realistic goal for ALL organisations of ALL sizes to operate local development environments using Vagrant and VirtualBox; a testing environment that spreads out the whole solution over multiple boxes (for testing networking code and configuration, among many other things); a staging environment for running performance tests (staging should match production bit-for-bit, cpu-for-cpu, ram-for-ram, ...) using jMeter or your choice of tooling; and finally a production environment to serve clients. This is the absolute minimum all organisations should be aiming for, and it doesn't even have to be fully automated using CI and/or CD.
Also tests, such as unit tests, systems tests, integration tests, usability and performance tests, and so on, are also critical to preventing the need to roll back and instead, implementing a roll forward policy.
Another option is to have customers point at stage after it has been upgraded and if it all goes horribly wrong, a load balancer change should be enough to point people back at the older production environment.
All this being said, problems in production shouldn't be a thing with configuration management, infrastructure as code (Terraform), and tests, not to mention three environments (development,test, stage - at minimum) to work your way through before pushing to production.
You'll still have problems, you've just automated them now. Those tools and approaches are great, but do they really prevent all production issues to the point where they "shouldn't be a thing"?
And a container management tool can facilitate handling a failed distribution automatically via rollback to a previously deployed working container.
http://www.se-radio.net/2016/01/se-radio-show-246-john-wilke...
There are plenty of caveats to the above (like the fact that the yum module won't downgrade [1], and you'll need reversible DB migrations) but that's basically the procedure.
[1] https://github.com/ansible/ansible-modules-core/issues/1419
I've completely mixed experiences with Ansible. Yes, it's easy to get started, but it's certainly annoying having to create playbooks for removing stuff to get a clean state.
Am I missing some other detail?