What are the three things Montmartre is best known for?
Montmartre is primarily known for its artistic history, for the white-domed Basilica of the Sacré-Cœur on its summit, and as a nightclub district.
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Montmartre is a safe neighbourhood. Down the hill, it's Pigalle which is the equivalent of the Red-Light district. As it is very touristy during the day and night you should not have any problems.
The area around Place Pigalle is seedy at night, but not all of Monmartre. The usual big city con artists hang out around Monmartre, mainly to take advantage of gullible tourists, but there isn't any major risk to your safety that you won't find elsewhere in Paris.