A quick Festo summary (with important details ignored and/or smoothed over):
Doctrine of Equivalents (DoE): the accused device doesn't infringe but should.
Let's start with an example. One of the areas where the DoE comes up is in claims with numerical ranges. Suppose a claim recites, among other things, that "the solution has a pH of no more than 2.0." Suppose the prior art showed the solution in the same situation (in the context recited in the remainder of the claim) has a pH of 7.0 or higher.
So, a competitor comes out with a competing product/process which uses a solution whose pH is 3.0. Do they infringe? Literally, no. But should it? Maybe. Under the DoE, it might.
Prosecution History Estoppel (PHE): you can't use the DoE to recover subject matter given up by amendment during prosecution.
Suppose the claim in the above example used to recite a pH of no more than 3.0 and the claim was amended to recite no more than 2.0. Applying the DoE to find infringement here would undo the amendment -- which seems to fly in the face of reason.
Flexible or complete bar? The law used to be that PHE represented a flexible bar. One case involving golf balls looked to see whether the accused device was closer to the claim as amended or to the closest prior art (or whether you could identify a hypothetical claim that is allowable and covers the accused). In my example, we have a claim of pH no more than 2.0 and prior art showing pH of 7.0 or more -- a rather large gap leaving a large degree of uncertainty. Should use of pH of 2.1 infringe? Probably. Should use of pH of 6.8 infringe? Probably not.
Festo established once and for all that PHE gives rise to a complete bar. In our example, the amendment from 3.0 to 2.0 means no DoE for the element of the claim at all. Not 2.1, not 2.01, not 2.0001.
The law used to require that the amendment was made in response to 102/103 rejections (in view of prior art), and not clarifying amendments in view of 112. Suppose the change was made from 3.0 to 2.0 because the description portion of the application didn't say 3.0, but said 2.0 instead (even if it was a clerical error). That used to not foreclose applicability of the DoE. Festo changed that -- any amendment for any reason related to patentability. What amendments are not made for reasons related to patentability? Well, sometimes I think I can make a claim broader and amend it accordingly.
Now, you don't even have to narrow the claim to invoke Festo. Narrowing a related claim is enough.
So, if you amend a claim for any reason, you can pretty much kiss the DoE goodbye.
So what? Why not just write the claim right the first time? I could go on and on about that. Let's just say that requiring absolutely perfect foresight and clairvoyance as to what art will be cited against you and all possible ways to capture the invention in claim language is a bit harsh. Many attorneys consider patent practitioners to be the best wordsmiths in the world and to have the toughest job in the legal profession, and many of us still fall short when it comes to foreseeing everything that could happen to each and every application we file.
Oh well, if it were easy to prepare patent applications, everyone would be doing it.
Regards.