Cockroaches, like many other insects use chemicals (like pheromones) for signals, such as visual, reproductive, tactile, and acoustic.
Four reproductive strategies are used in cockroaches. In most cases they will exhibit oviparity (laying an egg and leaving it to mature on it's own), or ovoviviparity (eggs are produced and mature within the mother). Viviparity (giving birth to live young) and parthenogenesis (asexual reproduction in which unfertilized eggs mature) also occur but in less species.
A study was done similar to that of Pavlov's famous dogs. And cockroaches respond too! When introduced a scent of vanilla or peppermint before sugar, the cockroaches eventually were conditioned to drool!
Cockroaches are fast!
The fastest cockroach ever recorded took off after 8.2 milliseconds after stimuli. In addition, its top sprinting speed is around 80 centimeters per second.
(References 8 and 9)
Cockroaches can live without their heads. Even after weeks, the cockroach will still respond to stimuli by wiggling its legs.
How can this happen? Nervous systems are not centralized at the brain in cockroaches., open circulatory systems prevent them from bleeding out, and they are able to breathe through spiracles on the body. They die usually because they dehydrate or mold!
COCKROACHES IN THE NUMBERS
Humans associate cockroaches with being only pests. However, we know that at least 4,000 species exist, and yet only 30 of those species commonly live in cities and with humans. It is well documented their ability to eat anything (including, but not limited to soap, paper, and hair). This is very important in natural habitats as they serve as nature's "trashcan" consuming organic waste.
GETTING THEIR VITAMINS
Cockroaches have a symbiotic (mutually beneficial) relationship with bacteroids. In exchange for hitching a ride in the roach's fatty tissues, the bacteroid will provide all essential vitamins and amino acids.