A fair bit. It's nearly all Roman-era and Byzantine-era. What we have from before the Roman conquest -- literary, philosophical, historiographical sources -- has, I suspect, pretty much all been translated.

The only real exception is fragments of early authors that survive in later sources or in papyri. By that I mean fragmentary quotations of authors like, say, Euripides, or fragmentary ancient papyri that contain bits of his plays. Some compilations of fragments have been translated -- lyric poets, Hesiod, Aeschylus --, but far from all.

Once you hit the Roman era, though, there are plenty of technical treatises of various sorts that no one's ever bothered to translate, because the only people who'd be interested in reading them are people who'd know ancient Greek already. There are also Christian tracts, scholia (commentaries), medical texts, and plenty more.

There are no projects to translate all this material. It isn't because of a dearth of scholars: there are plenty of people who can read and translate ancient (and Byzantine) Greek.

In the first place, there's way too much of it. There are slices of the Byzantine Greek literary tradition that haven't even been printed, let alone translated.

In the second place: money. No one is publishing translations because to print them, publishers would run at a loss. There's no money in it, and not much benefit. Take a moment to consider, for example, how much of a market there would be for translated editions of 10th century chroniclers, especially if a single volume cost hundreds of dollars (because it would). Who's going to be buying these $200 copies of Terentianus Maurus in translation?

Digitising manuscripts, however, is a different matter. That isn't anything to do with publishers: it's something that libraries do. And oh yes, they do it. On a library-by-library basis, mostly, though German libraries have been relatively organised about it and have nation-wide networks for rummaging around through manuscript collections.

Many European libraries with stocks of mediaeval manuscripts have digitised large swathes of their collections, or even their entire collections, and released them online for free. Others have not. Libraries are always highly motivated to make their material as accessible as possible, so where they haven't done so, it's mainly because of, again, money. The biggest leaders in digitisation, I'd say, are the Apostolic Library (at the Vatican) and the Bibliothèque nationale de France. But lots of other libraries in western Europe have digitised manuscripts online for free.