Responsive UI is one of the better design techniques for handling UI design for multiple screen sizes. There are a number of bootstrap solutions available; however, the nicest free package I’ve seen out there is the Responsive SharePoint project found on CodePlex. Many out of the box UI features have been customized to adapt to screen size such as the top navigation, quick launch, list views, and others.
At the time of this writing, the one major issue that appears is a “401 Unathorized” message that shows up when trying to browse to “_layouts/15/start.aspx”. From my experience with this solution the message shows up every second load of that page. Currently the way to get around this issue is to disable the “Minimal Download Strategy” feature, but if that is not an option for you, you’ll need to look for another responsive solution or create your own.
Overall a really good solution, and I’m looking forward to seeing this issue get fixed.