When a reductive group G acts on an embedded projective variety X, the associated coordinate ring C[X] is a G-representation. The data of this G-representation is recorded by the G-equivariant Hilbert series of C[X] and is algebraically equivalent to that of its K-polynomial or twisted K-polynomial. These polynomials are of independent interest, with connections to the minimal free resolution and multidegree of C[X] respectively. Non-cancellative combinatorial rules for the Hilbert series, K-polynomial, and twisted K-polynomial are all desirable. Although these three objects are algebraically equivalent, their combinatorics are distinct. In this talk we focus on determinantal varieties, where the combinatorics of pipe dreams and the Robinson-Schensted-Knuth correspondence naturally arise. We will present recent work (joint with Abigail Price and Alexander Yong) regarding combinatorial rules for the G-equivariant Hilbert series of generalized determinantal varieties, along with open problems and directions for future research.