These polynomials were introduced and studied by Shoji; they are analogues of Kostka polynomials $K_{\lambda,\mu}$ when $\lambda$ and $\mu$ are $r$-partitions. I will present a conjectural analogue of the Lusztig-Kato formula for Kostka-Shoji polynomials and their related geometric interpretation as multiplicities in the space of sections of certain vector bundles over flag varieties. I will also present another geometric interpretation of their stable version, as Poincare polynomials of IC stalks of a mirabolic version of zastava spaces (for $r$=2$).