While this does depend on style guide*, if you're typing a paper for a class (academic writing, with MLA, APA, or Chicago styles), you'll italicize the magazine title, both in your writing and in your citations.
- Ex.) In an article published by Vanity Fair last year, ....
- Ex.) National Geographic has been published since 1888.
Underlining in a digital format is used to indicate hyperlinks and should be avoided for media titles. If you're hand writing, however, then you would underline, since that's easier than writing in italics yourself.
* This is important! You will see it done in different ways in the wild.
For example, National Geographic and Encyclopedia Britannica both italicize the title of the magazine (which helps distinguish it from the society and the TV channel), while the Smithsonian's National Postal Museum does not. Each way is correct within its own context.
Meta-example: the website names just mentioned are not italicized, because this is writing for the web and not academically. In this context, people don't usually bother to italicize the names of websites, even though they would definitely be so in your academic citations and writing.
