More users use the Internet on mobile devices than on desktop and Google is going to make its search index mobile first. This should be the final wake up call if you don't have a mobile site yet.
I don't know how to stress this enough: make sure your website works on mobile. Period.
More than half of your visitors use mobile devices to browse your site and mobile Internet usage is still rising. Desktop web browsing is turning into a niche.
Google has pushed the mobile web forwards and recently Google announced that they are going to make their search index mobile first.
These are big news! If you aren't convinced yet, you should be by now. Make sure your website works on mobile. Period.
Mobile Friendliness on All Layers
Making your content responsive or mobile friendly is not enough. There are other things you should also consider for a mobile audience.
Just think about all the place where you use a mobile phone to access the Internet. In a car, on the train, in a cafe with lousy public wifi? See a pattern here? Although mobile Internet speeds have increased a lot in the recent years, you can't really trust your users to be able to download 100mbps reliably.
Nothing is more frustrating than a slow web experience. Make sure your server infrasctructure is as fast as possible and optimize content delivery for mobile devices. Remember to optimize your images and all static assets.