What do roaches eat?

unfortunately the little blighters can eat anything and they can live for months without food or water

I think we can get a little more detailed here! Roaches' favorite food is, of course, your leftovers. But they eat a lot of other surprising things:

• Paper and Glue: Cockroaches are known to eat paper and glue, especially if the materials are old or damp and moldy.
• Body Waste: These bugs can feed off the waste of people and animals.

They eat a few other things too - nasty buggers!

Source: http://pestcontrolexperts.com/blog/what-do-cockroaches-eat