BrowZine is one way to start keeping up with journal literature in your discipline. BrowZine allows you to browse thousands of academic journals by subject, easily review tables of contents, and download full articles. Stay Current by creating a personal bookshelf of titles to follow and receive new issue and new article notifications. Use the app to save articles for off-line reading or export to services such as Mendeley, EndNote, Zotero and more. Get access on your computer, mobile device, or phone. Download the app for Apple and android devices.
Periodical List also provides a Browse by Discipline feature.
Subject-specific databases also index journals within disciplines. Some databases also provide a list of journals included in their source. If you don't see the option, check with library staff for help.