I recently acquired a copy of Archbishop Annibale Bugnini's 'The Reform of the Liturgy'. If you want a 'horse's mouth' account of what they did, when, and why, in the liturgical reform, this is the book for you. Unfortunately, I find it so intensely depressing I can only read a few pages at a time... But it makes a reasonable reference book.
I was brought up on the idea that Eucharistic Prayer II of the New Rite of Mass (Novus Ordo: Ordinary Form) was this frightfully ancient and authentic text, 'the anaphora of Hippolytus'. It was a shock to read, in Michael Davies' 'Pope Paul's New Mass', that it is in fact a new composition, incorporating bits from Hippolytus, not in their original order, and actually rather a lot from the Roman Canon. But who'd believe him? This is what Bugnini says about it, on p456.
'The aim was to produce an anaphora that is short and very simple in its ideas. The anaphora of Hippolytus was therefore taken as a model. But, although many thoughts and expressions are derived from Hippolytus, Eucharistic Prayer II is not, as it were, a new edition of his prayer. It was not possible to retain the structure of his anaphora because it does not have a Sanctus or a consecratory epiclesis before the account of institution or a commemoration of the saints or intercessions. All these developed after Hippolytus and could not now be omitted in a Roman anaphora. In addition, various ideas and expressions in the anaphora of Hippolytus are archaic or difficult to understand and could not be taken over into a contemporary anaphora.'
So the 'Anaphora of Hippolytus' it ain't.
This is a theme running through the reform: things popularly promoted as being restorations of ancient prayers and practices are, in fact, so heavily adapted as to be unrecognisable, as well as being put into a completely different context, alongside things which have grown up over the centuries, and things which were entirely new. Mass 'facing the people' and Communion in the hand are obvious examples. In the case of the anaphora of Hippolytus, Michael Davies makes another point: it is not found in a liturgical book, and there is no way of knowing if it had ever actually been used liturgically. A funny kind of restoration this turns out to be.
Interestingly, St Hippolytus seems to have suffered a fate strikingly similar to that of his famous anaphora.