If you take one part gross, a bit of green and a pinch of functionality you are likely to end up with worm farming. Worm farms are in essence buckets of dirt and worms that you feed your leftover plant matter, card board and paper to. The moisture cause the materials to break down at which point the worms can dig in, eating your trash and enriching their underground home with nutrients. Think of it as a natural trash compactor with the added advantages of not requiring electricity and producing some of the best planting soil imaginable.
The worm farm in the video is called Can-O-Worms but there are DIY versions around as well. Just be sure to get the right kind of worms (Eisenia fetida) as some species are prone to escaping. Worm farms are a ton of fun and make a great weekend project for fans of invertebrates and would be fisherman.