Newspapers are being killed off by things like Craigslist. Most newspapers got their money from advertising - especially classified advertising - and that puppy has gone. Other free sources of news have been available for decades (TV and radio, for example), but it's the wholesale collapse of the small advert market that's done for the newspapers. There's a very good piece about it (and about the likely futility of paywalls, outside of specialist publications like the FT or the Wall Street Journal) here:
http://www.lrb.co.uk/v32/n24/john-lanchester/let-us-pay
It's from a few years back (December 2010), but a lot of it is still relevant.
Magazines are possibly a different prospect: with some notable exceptions, magazines were never as beholden to bulk advertising as newspapers. Reading long articles (like the one from the LRB, above) on a screen can be tiresome, unless you get it on a dedicated e-reader, and I suspect that dedicated e-ink e-readers will shortly go the way of the MP3 player, blown away by smartphones and tablets.
There are a couple of pieces from the Grauniad on the print magazine market - although both have been written with a definite bias towards the "print's not dead" angle:
http://www.theguardian.com/media-networ ... s-lifespan
and
http://www.theguardian.com/media/2014/f ... -isnt-dead
The whole industry is in a state of enormous flux (which statement takes the "No Shit Sherlock" prize for the tenth year running). But there are a lot of new developments which have still to shake out, like: will the public tire of clickbait news? It's the headline equivalent of those godawful jittering "You have new messages!!!" banner adverts from the earlier years of the internet. If the public wises up, and the advertisers realise that people in a state of artificially induced apoplexy are not in a prime new-bathroom-suite-buying mood, how will news sites lure in new eyeballs? And will Twitter ever actually make money?
The internet is a very good way of allowing people with specialised interests to find each other (viz. Oolite, these boards, etc.). As such, it's a very useful tool for identifying groups of people who might potentially want to receive, and physically own, well-made, well-written stuff about their particular hobby-horse. Which might imply that there's a decent potential market for, and an avenue for selling, well-made, well-written print magazines. There also seems to be a lot of highly talented people around whose skills and interests are under-used in their day-to-day lives (viz. Oolite, again). And very recent developments, like crowd-funded publication, show that it's possible to raise decent amounts of money on a promise.
Print technology means that shorter and shorter print runs, even litho, are more and more economically practical, and full-colour digital print is continually improving, allowing for the realistic possibility, in a couple of years, of producing high-quality magazines print-on-demand: sell one, print one, so no money is wasted in manufacturing unsold stock. Sustainability is still an issue, but that's always been the case.