From the Edo period, they started to be called "guardian dogs" in general in mainland Japan. Gender is variously assigned to the shisa. Some Okinawans believe the male has his mouth closed to keep bad out of the home, while the female has her mouth open to share goodness. Others believe the female has her mouth closed to "keep in the good", while the male has his mouth open to "scare away the bad". (Compare this to the distinction between male and female guardian lions in Chinese culture.) (from Wikipedia)
They even made their way into Godzilla films.