Renee Holtum interviews Jesse Shapiro on the topic of media bias and political bias in Econ Focus,  published by the Federal Reserve Bank of Richmond (2nd Quarter 2017, pp. 24-29).  The entire interview is worth reading, but here are a few points that caught my eye. The headings are my words, and the explanations are Shapiro.

Newspaper political bias is more likely to reflect readership, rather than bias of owners.
"What we were trying to figure out is which newspapers are right-leaning and which newspapers are left-leaning and by how much. In the context of the news media in the United States, there isn't really a training set. So we took an idea that was developed by Tim Groseclose and Jeffrey Milyo to use the Congressional Record as the training set. We have a lot of text by speakers who have a known political affiliation — what party they belong to and how they vote on issues. Then we find the phrases that are diagnostic of the speaker's party. We came up with things like "death tax" for Republicans and "estate tax" for Democrats, or "personal retirement accounts" for Republicans and "private retirement accounts" for Democrats, or "the war in Iraq" for Democrats and "the war on terror" for Republicans. We could then look for those keywords or key phrases in newspapers and answer the question: If this newspaper were a speaker in Congress, would it be more likely to be affiliated with the Republican Party or the Democratic Party? That's our quantitative answer to how right-leaning or left-leaning a newspaper is. ...
"What we found is that newspapers with a more Republican customer base are much more Republican than newspapers in more Democratic markets. And once you control for geography, there's very little evidence of an influence of owner ideology — whether you measure that by the positions of the other newspapers owned by that owner or by the owner's donations to different political parties. There really isn't much evidence that the owner plays a big role in how a newspaper slants the news.
There is less ideological segregation in online media than you might have thought. 
"Think of an online news outlet, like a blog, as a neighborhood, and let's measure who's in that neighborhood: What fraction of those people would self-identify as conservative? What fraction would self-identify as liberal? And let's calculate how segregated is this universe, how segregated is the Internet. To what extent are people visiting news sites that are only populated by other people like them ideologically?
"We found that the extent of segregation on the Internet is surprisingly low. It's certainly true that people gravitate to like-minded sources. So for example, foxnews.com has a more conservative audience than nytimes.com. 
"But the Internet is not radically different from traditional media. Take the fraction of the audience on a given news site that is conservative and call that the conservativeness of the site. Then take the website visited by the average conservative on the average day — that website is about as conservative as usatoday.com. Now do that same thing for the average liberal, that's about as liberal as cnn.com. If you were to read those two outlets, you wouldn't find that they're radically different.
"In fact, we find that isolation is very rare in the data. We have individual-level data on users on the Internet. People who get all of their news from outlets to the left of, say, the New York Times are very unusual. Likewise, people who get all of their news from sites to the right of Fox News are extremely rare. Folks that go to a fringe conservative site like rushlimbaugh.com are more likely to go to nytimes.com than readers of Yahoo News. The people who are consuming niche media are probably pretty politically engaged people, and therefore they want to read a lot of things. So in the end, the picture is a lot more muted than what people have feared."
Use of online news and social media is not correlated with political polarization. 
"We just compare trends in polarization for groups of people that have high or low propensities to use the Internet and social media. Our favorite and most important comparison is with respect to age. People who are 75 years and over rarely use social media and don't report getting a lot of political information online. People who are 18 to 25 frequently use social media and report getting a lot of political information online. So if you thought that social media was contributing to the rise in polarization, what you would expect to see in the data is that polarization is rising especially fast for younger Americans — and if anything, the story is the opposite. The rise in polarization is similar between the relatively old and the relatively young, and if anything, maybe polarization is rising faster among the relatively old. So in that sense the data don't line up with the hypothesis that social media is driving the rise in polarization.
"I think the effect of the Internet on polarization remains an open question. We're arguing that it doesn't appear that social media is accounting for the increase in polarization, but we haven't offered a constructive account of what is driving it. Until we have a better understanding of that, it's hard to rule anything out."
Political phrases have become more specialized and identifiable by party affiliation over time. 
"So what we did is try to figure out, for every session of Congress and every point in time, how easily a neutral observer could tell whether someone is a Republican or Democrat based on how they talk. We took the entire Congressional Record and used computer scripts to turn it into quantitative data about the use of phrases. Then we took the counts of phrases by every speaker and every session of Congress back to the 1870s and fed that through a model of speech. The model can tell us, at every point in time, how informative your speech is about your party.
"What we find is that in the 1870s, if I give you a minute of random speech from somebody in Congress, you're going to guess his party correctly about 54 percent of the time, only modestly higher than chance. In the late 1980s, you'd be doing a little bit better, but barely. By the 2000s, the number is closer to 75 percent. Something enormous changes between the late 1980s and the 2000s to cause the parties to diverge tremendously in how they're talking — many more phrases like "death tax" and "estate tax."
"The timing of the change coincides with the "Contract with America" and the Republican takeover in the 104th Congress in 1994. That was a watershed moment in political marketing. It showed the power of language to frame a set of issues and craft a narrative that could be very powerful in winning elections and changing policy views. In the wake of that, strategies on both sides crystallized around trying to have a very consistent message and use very consistent language to try and influence how voters saw the issues. I think that's what's reflected in the data.
"In terms of implications, one speculative possibility is that the fact that Republicans and Democrats are speaking differently to each other might contribute to hostility. It might make it harder for them to find common ground or recognize positions on which they do agree. That's not something that we show in the study, but that's one not-so-optimistic possibility suggested by it."