  We review the recent developments of the SUSY quantum Hall effect
[hep-th/0409230, hep-th/0411137, hep-th/0503162, hep-th/0606007,
arXiv:0705.4527]. We introduce a SUSY formulation of the quantum Hall effect on
supermanifolds. On each of supersphere and superplane, we investigate SUSY
Landau problem and explicitly construct SUSY extensions of Laughlin
wavefunction and topological excitations. The non-anti-commutative geometry
naturally emerges in the lowest Landau level and brings particular physics to
the SUSY quantum Hall effect. It is shown that SUSY provides a unified picture
of the original Laughlin and Moore-Read states. Based on the charge-flux
duality, we also develop a Chern-Simons effective field theory for the SUSY
quantum Hall effect.
