it started in Britain in the Middle Ages. 'Halloween' is a corruption of All Hallows' Eve, when kids would go out 'guising'. It was a celebration of dead relatives. They dressed as ghosts, carried a hollowed out turnip with a candle in it and knocked on people's doors. They asked to do a service for the owner, for which they received a small treat.

Istarted in the US in the 1930's. Obviously now, the Americans got into it big time and introduced loads of other customs and made their own inputs with monsters and stuff. It's probably more of a US thing nowadays (culturally). It gets bigger every year here.

I only know all this because I was researching for a pub quiz I am running.