Founded in 1893, there are nearly 400,000 volumes, including 25,000 rare books, 11,000 manuscripts and more. It also has 40,000 fragments from the Cairo Genizah, a collection of international ketubot (Jewish wedding contracts) and Passover haggadot. The library also has the world's largest collection of early books printed before 1501.
The JTS Library has just started a blog - JTS Library Takeaway - to be based on questions received at the reference desk. The librarians will post comments and suggestions and invite readers to provide their input on the answers.
There are just a few postings, but I'm sure it will grow. There seem to be a lot of food-related questions, but that's what people asked. One post indicated receiving e-mail questions, so that's another route for researchers with questions about sources.
When I was working on our DARDASHTI family project, I contacted the library for Persian Jewish history sources. Everyone was extremely helpful. It is always worth checking the catalog or contacting the Library to see if materials pertaining to your family - no matter its origins - might be among their holdings.