As fond as I am of books, a great deal of information can be found online these days thanks to many digital archives. We even have digital libraries now like Google Books (books.google.com ), Gallica (si on parle franÃ§ais: https://gallica.bnf.fr) and Hathi Trust (https://www.hathitrust.org/), the Library of Congress (which includes many resources including a digital sheet music archive, photos, and so much more https://www.loc.gov/ ), a number of university archives (Harvard, etc.) and of course the Petrucci Music Library (https://imslp.org/wiki/Main_Page). Some of these make available resources that were difficult to impossible to access just a few years ago.
In addition, we have the archives of several theaters that have been digitized. Alas not all the major opera houses have made this information available online, but a few have. BCBCers are likely aware of the Metropolitan Opera Archive that Derrick Goff showed us a few weeks ago during a Sunday MatinÃ©e. (https://www.metopera.org/discover/archives/). The performance database is especially useful as it includes not only casting for every performance the Met has ever given (including concerts), but also links to reviews of those performances. (http://archives.metoperafamily.org/archives/frame.htm) This makes it easy to research the performance history of any opera at the Met, compile a list of which roles any given singer sang there and other information.
For example, one thing that interests me are operas that were once quite popular but are now rarely given. So doing a search of the Metâ€™s hit parade (http://archives.metoperafamily.org/archives/frame.htm) we find that the all-time most performed operas at the met are La Boheme, Aida, La Traviata, Carmen and Tosca. No surprising there although there was a time when the top three were ABC (Aida, Boheme, Carmen) which shows how preferences have shifted a bit over time. If we scroll down further, we start to see operas that were performed dozens of times but have not been heard at the Met in decades. At the top of that list would be Les Huguenots (129 performances between 1884 and 1915), Martha (116 performances between 1884 and 1968), and Mignon (110 performances between 1883 and 1949). The data is also searchable by opera and by performer. You can even find a list showing which performers sang the most performances. (Spoiler alert: singers who performed character parts top that list as they often sang several nights a week over multiple seasons.)
Of the Italian theaters, there are excellent archives for both Veniceâ€™s Teatro alla Fenice (http://www.archiviostoricolafenice.org/ricerca.php) and Milanâ€™s Teatro alla Scala (https://www.teatroallascala.org/archivio/ricerca.aspx?lang=en-US). These allow us to see the history of repertoire and performances in those houses. For example, Rachelle Jonck stated during last weekâ€™s Sunday MatinÃ©e that Il barbiere di Siviglia was the first opera never to fall out of the repertoire. Well, with these archives we can see just how true that is, at least in Venice. At La Fenice (http://archiviostorico.teatrolafenice.it/ricerca.php?q=Barbiere&Tipo=opere) we find a performance almost (but not every) decade since its premiere there (with a recent and somewhat curious gap from 1979 to 1995). La Scalaâ€™s information does not go back before the mid-20th century, nor does that of the Wiener Staatsoper (https://archiv.wiener-staatsoper.at/), but both are useful for more recent performances.
Sadly, the Paris OpÃ©ra has not digitalized its archives, but the OpÃ©ra-Comique has (https://dezede.org/dossiers/archives-opera-comique/data). This is another useful archive with links to information about the operas and their performances and casts. It was here that I found information about an opera Adolphe et Clara in which Gabriel Duprez performed several times just before leaving Paris for a multi-year stint in Italy. https://dezede.org/oeuvres/adolphe-et-clara-ou-les-deux-prisonniers/ If you are looking for information about lesser-known French operas, this is an excellent resource and like the La Fenice database includes links to images of the original posters announcing the performances. In some instances, there are even digitized copies of the original documents necessary for getting the production past the French censors.
One last very useful database for current performances is Operabase (https://www.operabase.com/en). I have often used this to find information about current productions (has anyone produced a certain opera recently) and current casting trends. Or perhaps you would like to know which houses have performed Handel recently or have upcoming performances of operas by Meyerbeer. You could also search if you were wondering what roles someone who sings repertoire similar to yours also sing, this is the place to look. (That approach is not foolproof, obviously, but it is a good way to get some fresh ideas for repertoire.)
At this point, it should not be assumed that you have to go onsite to gain access to historical documents. In some cases, you do, but increasingly libraries are digitizing their collections. I likely missed some excellent online archives, and new material is becoming available all the time, so if you know of any good ones that I omitted, please let me know. In the meantime, happy researching!