The rank $n$ superspace is the algebra of polynomial-valued differential forms on affine $n$-space. This carries a natural action of the symmetric group, or in general, of any pseudo-reflection group. The superspace coinvariant ring is the quotient of superspace cut out by elements that are invariant under this action, and have a vanishing constant term. Due to their interesting combinatorial and representation theoretic features, these objects have received a lot of attention in recent years. In this talk (based on joint work with Brendon Rhoades), I will go over some recent progress in understanding superspace coinvariants for an infinite family of pseudo-reflection groups, and some natural questions that remain open.