This talk describes a method to compute supersymmetric tree amplitudes and loop integrands in ten-dimensional super Yang-Mills theory. It relies on the constructive interplay between their cubic graph organization and BRST invariance of the underlying pure spinor superspace description. After a general introduction to this kind of superspace, we discuss a canonical set of multiparticle building blocks which represent tree level subdiagrams and are guided by their BRST transformation. These building blocks are shown to yield a compact solution for tree level amplitudes, and the applicability of the BRST approach to loop integrands is exemplified through recent examples at one-loop.