The works to be digitised include the small but staggering collection of Greek manuscripts in the Vatican, including ancient texts of works by Homer, Sophocles, Plato and Hippocrates. The Bodleian's collection is much larger – by the end of the 17th century the most important in Britain – but later, mainly of 15th and 16th century manuscripts.The project website is here. Note also its Hebrew Manuscripts page, the essay thereon by renowned Hebrew codicologist Malachi Beit-Arié, and the essay by Nigel Wilson on the Greek manuscripts.
The Vatican's Hebrew texts include the oldest Hebrew codex – a manuscript bound as a book – in existence, and a copy of the entire Bible written in Italy around 1100. The Vatican's collection of 8,900 incunabula – the earliest printed books, many published in Rome – is the fourth largest in the world, followed closely by the Bodleian's.
Background here, with lots of links about other digitization projects.