Set in a valley with two small greens and one larger central green, the village was recorded in Domesday as "Saham". The settlement was once owned by the Bigods, Earls of Norfolk hence the name. The brewery is now located behind the village shop, not the pub.
Mill Hill marks the site of a late 17th century post mill which worked until 1917 and was demolished in 1947, though some parts were incorporated into a home. Another post mill off Low Road was also demolished in 1947.
The A1120 through the village follows the route of an old Roman road. Unusually for such a road, it isn't completely straight - the kink being due to a lake that was in the way.
Some historical information from English Heritage's National Monuments Record.