Super-Poincaré covariant quantization of the ten-dimensional superstring has recently been achieved using a BRST operator constructed from a pure spinor variable. Starting with the simpler case of the ten-dimensional superparticle, I review this quantization method. I then use this new formalism for the superstring to compute manifestly super-Poincaré covariant N-point tree amplitudes and to construct a quantizable superstring action in an AdS_5 x S^5 background with Ramond-Ramond flux.

References : hep-th/0001035, hep-th/0105050, hep-th/0004171, hep-th/0009168