This talk is about recent work with Luc Lapointe of the Universidad de Talca in Chile. I will present what it means to be a Schur function in superspace and what properties they have. One of the first steps to building a theory of symmetric function theory in superspace is to describe the Pieri rules for these superspace versions of Schur functions. In our research, we have described them and proved that they are correct. Furthermore, we have just started to study the Pieri rules for the Jack polynomials in superspace as a stepping stone to understand the Pieri rules for Macdonald polynomials in superspace. We uncovered a surprise connection to the set of alternating sign matrices and the partition functions of square ice!!!