The tests for year six pupils are meant to see how well children are doing in reading, maths, spelling, punctuation and grammar.
But some teachers say that schools and pupils didn't know about some of the marking rules, and they aren't always being applied properly anyway.
One example given seems to show a pupil losing marks for writing a letter in an answer box too untidily...
Another shows a student losing marks for making punctuation too big when it's being added to a sentence.
Some schools also say there are also examples of questions being marked as wrong for some pupils and as correct for others.
Teacher groups don't think it's fair to mark children according to rules they say no one knew about, and that 'correct' answers shouldn't be marked as 'wrong' over small mistakes like these.
The government says they believe the tests are fair but that getting the marking right is really important.
They say head teachers can ask for marks to be reviewed if they think there's a problem.
Teachers are complaining about the way that the Sats have been marked this year.