The nasty thing about roaches, is that if you've seen one in your home, this probably means you have high population densities and an infestation. They're nocturnal, and given that they can flatten their bodies, can be found almost anywhere, even under mats and behind cabinet and wall papers. When the populations are large enough, or a sudden drop in food occurs, they have been known eat human flesh, though this is rare and fairly extreme. The biggest danger is quite simply that they spread disease, all across your pillows, dishes, and even - yes - your toothbrushes.
Unfortunately, like bedbugs, cockroaches are also one of the infestations that are extremely hard for the average individual to knock out. This is largely due to the hardiness of the bugs, as well as needing professional knowledge of their habits, what works, and having access to the right tools to get the job done.
Roaches can fit through the smallest of cracks - as thin as a dime.
Here's a video to a particularly bad roach infestation. In situations like this, you have to be exceedingly methodical, inch-by-inch throughout the house, inside walls, inside furniture, and if this is an apartment - the entire building. This level of infestation would probably require multiple treatments, over a month or two.
Roach racing in Vegas - roaches are some of the fastest insects, at 50 body-lengths per second. That's equivalent to a human running 210mph.
Roaches can live for a month without food, a week without water, and can hold their breath undewater for over 40 minutes.
Additionally, roaches also need a fairly consistent plan and partnership over several weeks, between exterminator and client. Partly, eliminating roaches is a matter of eliminating the habitat and resources they need to survive - consistently keeping your home in spotless shape for a few months, with no food or water for them to thrive on. Given that they can go months without food though, this is only supplemental to attacking them on multiple fronts with different tools - everything from pesticides and traps to heat guns and vacuums. Every situation needs a customized solution, however. These are some of the toughest infestations out there to kill off.