Overrun means being populated in huge numbers or occupied in some way. Your beautiful beach town may be peaceful in the winter but overrun by tourists every summer.
You can use this verb for a successful invading army: "The troops managed to overrun the entire peninsula, reclaiming the land they'd lost." It's also good for other kinds of invasions and infestations: "They closed my dog's daycare because it was overrun by fleas." The earliest meaning, still used today, was "continue beyond a specified time," like the class that overruns by fifteen minutes, making you very late to third-period math.