In this talk, I will review basic features of the pure spinor superstring as well as recent progress to compute and compactly represent scattering amplitudes in this framework. A string-inspired organization scheme for amplitudes in both field- and string-theories will be described where the non-linearities of ten-dimensional super Yang-Mills theory are encoded in so-called multiparticle superfields. They allow to efficiently capture the polarization dependence through cubic diagrams where the intuitive mapping as well as the composition rules for amplitudes are guided by BRST invariance.