We study the N=1/2 supersymmetric theory on noncommutative superspace which is a deformation of usual superspace. We consider deformed Wess-Zumino model as an example and show vanishing of vacuum energy, renormalization of superpotential and nonvanishing of tadpole. We find that the perturbative effective action has terms which are not written in the star deformation. Also we consider gauge theory on noncommutative superspace and observe that gauge group is restricted. We generalize the star deformation to include noncommutativity between bosonic coordinates and fermionic coordinates.

19 pages, 6 figures, JHEP class, footnotes added, typos corrected, version to appear in JHEP