I use Zotero as my primary bibliography manager. It is an open-source, freely available program (compared to its alternatives such as Mendeley, Endnote) but works equally well.
Using Zotero with online plugin allows you to save any journal paper or link to your offline library with the full-text PDF. It also detects and works through proxy-redirection of your institution to provide access when accessing from outside. Further, you can access your library at any device by syncing your library to Zotero online file storage.
However, the online Zotero file storage only provides 300 MB of storage, which is not hard to useup. There are many alternative ways to setup file-storage syncing with non-Zotero servers or services, and I found one that works quite well.
Box is an cloud-storage service just like Dropbox or Google-Drive. They are popular and well-trusted service providers. But the good part is, they offer a 10GB of free storage as well as WebDAV support for use with Zotero.
WebDAV support allows Zotero to directly use the Box-account as its file-storage. In this way, you can not only sync and have your files available at all your devices, but also not have to worry about 300 MB limit.
Once you have your WebDAV account info, enter the URL provided by the service, your username, and your password in the Sync preferences tab. Be sure to select 'http' or 'https' as appropriate — if you're not sure, try 'https' first. After entering the information, click “Verify Server”. If Zotero successfully verifies the WebDAV account, you're all set to use file syncing via WebDAV.