For those interested in SEO (and who isn't) please see the this article in SearchEngineWatch. In the past Google has adjusted its algorithm on a periodic basis which has caused some surprise and dismay among some companies when they find themselves suddenly relegated.
The subject of Mobile Friendliness is, unfortunately, rather detailed. Please be aware that "being responsive" and "being mobile friendly" are not the same thing. Some studies claim to show that responsive sites actually contribute to a poorer user experience ... others show the opposite.
For the sake of pure pragmatism and for those less interested in the ins and outs of this discussion, do make sure to follow the links in the article linked above to Google's mobile friendly test.
But also please be aware that sites that would benefit from better mobile optimisation seem to pass this test. If your site varies its layout but doesn't adjust what gets sent to the device you may well be sending things to the mobile user that have unnecessary and undesirable cost and performance implications. If you're interested in improving user experience rather than just checking the SEO box, please also look at Google's PageSpeed.
Also check out the Chrome Developer tools which simulate your site experience on various screen sizes and under various typical network conditions (3G etc.) - hamburger icon | More tools | Developer tools | phone icon - in your Chrome browser.
Recent news on responsiveness:
The BBC attracted quite a lot of criticism for its recent "move to responsive".
The following is a relatively-speaking polite debate on the topic between religious adherents of both sides of the argument, from the extraordinary Bruce Lawson.
For those with a deeper level of interest in Web technology: among the comments on the above from the great and the good of the Web world please note in particular that of Andrew Betts of the FT. You may or may not remember that the FT famously eschewed an app-based approach in favour of Web only. They know a thing or two about this topic.