  I review and discuss the construction of supersymmetry multiplets and
manifestly supersymmetric Batalin-Vilkovisky actions using pure spinors, with
emphasis on models with maximal supersymmetry. The special cases of D=3, N=8
(Bagger-Lambert-Gustavsson) and N=6 (Aharony-Bergman-Jafferis-Maldacena)
conformal models are treated in detail. Most of the material is covered by the
papers arXiv:0808.3242 and arXiv:0809.0318. This is the written version of a
talk given at 4th Baltic-Nordic workshop "Algebra, Geometry and Mathematical
Physics", Tartu, Estonia, October 9-11, 2008, to appear in the Proceedings of
the Estonian Academy of Sciences, vol 4, 2010.
