An operator basis in a QFT captures the outcome of all possible physical experiments. However, constructing a basis is not easy. I will describe a polynomial ring construction using what are known as momentum spinor-helicity variables, and how the conformal algebra can be used to organise the basis. Primaryoperators (annihilated by special conformal generator) play a special role; they have support on a Steifel manifold, and I'll describe what we so far understand about their explicit construction. I'll also talk about things I don't yet understand (or at least can only get at via computationally difficult methods).