Consumer Reports is running an article titled Free Over-the-Air TV Is Going to Get Better [consumerreports.org]. They're rolling out a new standard, ATSC 3.0.
According to the article, you'll be able to watch OIA TV on your phone or tablet! I wrote an article a few years back wondering why you couldn't already.
It's a fairly long and very informative article worth a read. It only talks about American broadcasts, no word about when or if it will reach other countries, but my guess is it won't be long.