How to manage multi-project Trello boards

I've been using Trello since its launch in 2011, mostly for personal productivity, and small single board projects. I was very happy with out of the box functionality, but some time ago I've started using it in a special team which worked on more than fifteen projects simultaneously and realized that I need a way to manage backlogs of different projects on separate boards, but still have the main board for tracking work in progress, as easy and usable as if it was all one board.

Basically, I needed something like this: