Also bonus - support latex and bibtex. You can highlight in the pdf, and zotero will extract those highlights and add them to the entry as notes. Very handy.
And for mobile, i use this seemingly now-abandoned app called papership [ios][0]. It lets you signin to zotero and your webdav provider, so you have a sync of books/papers, along with your highlights, notes and whatnot. Thankfully, it seems like zotero are hiring ios devs, so a first party app might be on the horizon.
[0]: https://www.papershipapp.com/
edit: seems like papership recently started getting updates again, so its not abandoned anymore.