Prikry type forcing is the standard way of constructing models of the failure of SCH. On the other hand the negation of SCH is at
odds with the failure of the weaker square principles. I will go over both some classical and more recent consistency results
about obtaining the failure of SCH and failure of squares. Then I will present a dichotomy theorem, joint with Spencer
Unger, characterizing what type of Prikry posets add weak square.