Tattooing is an important tradition in the Maori culture. In the past, women would usually tattoo their chin and sometimes their lips. This has some reference to being wise and passing along important information and traditions within the tribe. Even now, we occasionally see older women in the streets with tattoos on their chins.
The men would have the genealogy of their mother tattooed on one side of their face, and that of their father on the other side, so obviously the sides were not symmetrical. When meeting a stranger, one would know instantly his tribe and ancestry. (In more recent times, men opt for a symmetrical pattern of their own choosing.) Tattooing was a matter of great pride, honor, bravery, etc. and women would not marry a man who was not tattooed. It was a very long and painful process, sometimes going deep enough to etch bones and many times rendered the recipient unconscious during the process.
(Side note on the above picture: I think I've mentioned before, that men perform the haka in which they portray confronting an enemy. Part of the dance is to appear fierce in order to intimidate and they do this with swift movements of their weapon, bulging eyes and tongues stuck out. They dance or move with all parts of their body.)
The tradition of tattooing continues today and we see many, many, many people with tattoos, but usually not on the face. We see many people, mostly men, with tattoos that cover their entire arms, or legs with very intricate and distinctive designs rather that a specific object.
The above photos were taken at a Maori tourist attraction, so I'm not sure if their tattoos are real or painted on, but I've included the following photo taken at a local farmer's market that I think I've posted before, to show real facial tattoos: