In this talk we shall review the pure spinor approach for the super-Poincaré BRST covariant quantization of the superstring. We will focus on the BRST operator, its cohomology and the computation of central charges in the pure spinor conformal field theory, where the ghosts are constrained to be pure spinors. This will mainly review work due to Nathan Berkovits and will be at a broad/informal level.

References

1. Nathan Berkovits, ICTP Lectures on Covariant Quantization of the Superstring,
   hep-th/0209059
   
2. Nathan Berkovits, Covariant Multiloop Superstring Amplitudes,
   hep-th/0410079
   
3. Nathan Berkovits, Nikita Nikrasov, The Character of Pure Spinors,
   hep-th/0503075