The Google have been warning about this for a couple of months, and have provided guidance to web developer dweebs on how to make sites responsive.
This page https://www.google.com/webmasters/tools/mobile-friendly/ will allow anyone to test the responsiveness of any site. And the page also provides the guidance and information on how to make a responsive site.
But many sites might see their search rankings (and therefore traffic to their site) get demoted for visitors using a mobile device for searching. Note that a desktop search will not result in affected ranking, although I suspect in the future.
I do a lot of web sites. This site passed the test: it shows that the page is “mobile-friendly”
But anyone that has a web site that relies on search traffic (and revenue) will see reduced search visitors because of this new ranking algorithm for mobile searches. They will need to scramble to get into a responsive mode.