Google just announced they'll be re-jiggering their algorithm to give a bit more emphasis to mobile-friendliness. This will happen some time around the beginning of May. If you haven't already setup a mobile-friendly or responsive site, then please get on that right away. If you have a mobile-friendly site, but want to go the extra mile, then I suggest you start working on implementing Accelerated Mobile Pages (AMP).
Accelerated Mobile Pages are a page type announced by Google in late 2015 and designed to serve mobile content faster by stripping out some code and tags. AMP has been adopted by several publishers including the Guardian and Google has worked with WordPress, Drupal and other publishing platforms to make it widely available.
Here's a video overview of the project:
What Should You Do?
If you don't know if your site is mobile-friendly, then start by using Google's Mobile-Friendly Testing Tool to get a better grasp of your website situation. If everything looks good there, then start thinking about how to get AMP setup.
Right now, I'm working on AMP using the WordPress plugin. I am troubleshooting some issues right now (more on that soon), but installing the plugin only takes a few minutes. If you're using WordPress, then download the plugin, install it, and go here to get AMP reports added to Google Search Console.
I will share more when I know more.
Also published on Medium.