Very interested in this feature, especially when it comes to using Mathematica with high school students who have no conception that a program might not include undo functionality.

Agreed, input-text-undo would be terrific and needed.

Completely agree, just text Undo would be great.
Here is the Stack Echange post relatad to Undo. A very popular one.

It speaks to the power of Mathematica that so many users tolerate the lack of an UNDO command.  What other companies could get away with "I know all of our users want it, but it's too hard" after 9 versions?

The stomach is not involved. Interesting things are in the private SVN. Then there is a working directory and a copy directory for meaningful notebooks. That gives some old fashioned fall back security. Duplicating cells (original cell and working cell) in a notebook is poor man´s solution. Mathematica punishes the evangelists of happy flow like many other instances on earth do. IMHO an even humble undo would be far more useful than this infamous incredible suggestion bar.

I'm relatively new to Mathematica, and whilst I am in awe of its fundamental mathematical capabilities, the lack of front end support for multiple levels of undo is an equally aweful oversight. If I, as a relative beginner, am already so frustrated that I should even contemplate learning the front end implementation in depth just so I could implement an undo feature myself, you may imagine just how important to me this omission is. Yes, I have already found and signed the petition but further comment is still warranted.

I come from a business and IT background, and have worked on complex turnkey systems and major software developments, so I do appreciate that if it has not been done already, Wolfram have reasons for not doing it. What seems to be missing is a detailed capability and impact analysis that users could review and contribute to in order to define the scope of undo/redo that would satisfy most with least effort and risk for Wolfram,

Since I have had to think about the issue of undo/redo and history management generally in other contexts, I recognise that it is not trivial, but neither do I think that multiple undo/redo in input cells should present particularly great difficulties. I am sure that more experienced users could make valuable contributions if there was a suitable public discussion.

As a side commnet on front end weakness, the global scope of "Replace All" in "Find and Replace" is a disaster that has already heppened to many it seems. Surely "Repalce All in Selection" could be added!

I am running 14.0 and built-in multi-step undo seems to work with small notebooks. With my larger notebook size 30k, 900 lines, I only get one level of undo, sometimes zero.

The problem seems to be MemoryLimit = 10,000,000 is too small. It took a while to find the option. It is Format/Option Inspector/Editing Options/Private Editing Options/UndoOptions. It took a few tries to get it set as a GlobalOption. You can only set it to Infinity with the dropdown. If I change the value to a different value it just gets changed back. Once I set it to Infinity, you have to unclick a dark box in front of the option to set it back to a value. The only possible value seems to be 10000000.

Having set this to Infinity, I am getting multiple levels of undo. More news as I use it more