In 2014, Minac and Duy Tan showed that triple Massey products vanish for the absolute Galois group of any field F. In 2019, Harpaz and Wittenberg showed that this remains true for all higher Massey products in the case when F is a number field.  The first natural case to consider beyond fields is that of Massey products over curves over fields.  I will discuss some known and new vanishing and non-vanishing results in this case.  The main tool is the representation theory of \'etale fundamental groups into Heisenberg groups.  I will begin with background about Massey products, which first arose in topology, and about the relevant representation theory. This is joint work with Ted Chinburg and Jean Gillibert.