When it comes to typeface, The Atlantic has a consistent, educated feel across all of its issues. Take this example of a FOB story about Lolita. It shows the general pattern of typography for the magazine – the department name, headline, and dek are serif (Lyon Display and Lyon Text), while “The Omnivore” and byline are sans serif and in all caps to set them apart (Rajdani). This helps create hierarchy by differentiating the parts of the page. Sans serif is used sparingly, but I think use of sans serif helps give the magazine a more modern feel since serif can feel too old fashioned. Often, headlines in the well are sans serif, which makes them stand out from the body copy, dek, etc. Meanwhile, the body copy is almost always serif, which makes for a easy read and also gives a sophisticated, educated feel to the magazine. 
Pull quotes are almost always sans serif, bold, and significantly larger than the body copy, set aside by white space. All of these factors help draw the eye to the pull quote.
Every once in awhile, though, The Atlantic breaks its general mold. For sidebar stories, it usually does almost the exact opposite – headlines and body copy in sans serif, with the dek in its serif choice. Overall, this helps the sidebar story stand out from the other stories and because they aren’t too long, having a sans serif body doesn’t affect the reading quality too much. 
See the example for “The Science of Sibling Rivalry.”
Overall, these typographic decisions help create hierarchy and make the reading easy on the eye. The serif choice for most of their copy makes reading flow well (especially considering their many long-form articles) and also gives it an educated feel.
