While presenting an End user workshop I was asked about Responsive Design and SharePoint Online.
As I researched this more I discovered how it is already in use at Microsoft and I did not even realize it. I also came to realize that it is built into our O365 Theme already, you can see this by looking at the screenshots.
As well MSIT has developed several portals using the Responsive Design, and they have composed some information around this in there Microsoft IT Showcase
Here is an interesting blog about SharePoint and Responsive Frameworks like Zurb or this, the general idea being that while the frameworks are great they add to much bloat for a production environment and you need to clean up many objects before taking them to Production. And to give you an idea of how to create a responsive masterpage please see this article.
As well I would like to remind you that when customizing SPO we recommend using the SharePoint extension framework, using that framework you can use the same knowledge about responsive design that you acquired over the years to build your website, see this article.