Cockroaches are scavengers. While most roaches prefer sweets given a choice, in a pinch, they will eat just about anything: glue, grease, soap, wallpaper, paste, leather, bookbindings, or even hair. Worse yet, a cockroach can survive a remarkably long time without food. Some species can go as long as 6 weeks without a meal! These traits make cockroaches in our homes tough to control. But in nature, cockroaches provide an important service by consuming organic waste. They're the garbage collectors of their habitat.