The list of terrific electronic resources that help with papyrological research is long. The annotated list here contains but a selection of the most important starting places, sites that you should get to know. We will also as a class work on accumulating a more extensive list of important papyrological tools (see below).
Checklist of Editions of Greek, Latin, Demotic, and Coptic Papyri, Ostraca and Tablets
This is the essential key to understanding abbreviations of papyrological editions. Started by Duke’s own Bill Willis and John Oates, it continues to be maintained by colleague Josh Sosin, with the help of others. The papyrology room uses these abbreviations as the basis for organization, so this resource is critical to finding your way around in that room.
Leuven Database of Ancient Books (LDAB) - Trismegistos
Now the standard starting point for finding fragments of ancient bookrolls and other literary and para-literary texts. The umbrella site (Trismegistos) is also an amazing tool, well worth exploring, though more useful for documentary studies. You’ll find lots of references over time to Pack's old print catalogue of literary papyri, or to the second edition, Mertens-Pack, and this is now an online facility with much more extensive bibliography than LDAB (though otherwise more limited): this is known as MP3, Mertens-Pack online.
The so-called “Papyrological Navigator” is the basic portal for work on papyrological documents. Important for our purposes, since it includes letters. This extends the work of the Duke Data Bank of Documentary Papyri, started by Duke's Willis and Oates back in the 1980s, and is headed by our own Josh Sosin. (You can also use this to get at literary APIS records, but it’s not very intuitive.)
Since the Papyrological Navigator focuses so much on documents, other views can be important for retrieving information on literary texts. Much the richest set of resources is often found in the catalogues for individual host institutions. These are a few I find particularly useful:
Oxyrhynchus Online - an important resource for images of the Oxyrhynchus papyri, which is far the largest repository of literary remains on papyrus
Duke Papyrus Archive - old but still useful for understanding better the contours of the Duke papyrus collection. Mostly put together by Peter van Minnen.
Yale Papyrus Collection - an important collection and a very thoroughly done site, perhaps the most complete [no longer accessible August 2018!]
Michigan APIS portal - an important collection, and a good site, but unpublished papyri often have restricted (i.e. no) access to the images
IFAOGrec Unicode - the now-standard unicode extension with the full set of characters needed to edit papyrological texts - information and download
pappal - though focused on documentary hands, pappal is an indispensable tool, since it hosts a complete collection of the images of dated documents on papyrus
Other useful links
The papyrus pictured at top is P.CtYBR 5018, a literary papyrus from the Yale collection, published by Johnson in 2016.