In this talk, I will focus on a new construction of boundary correlators (or wavefunction coefficients in dS) that highlights simplicity at all spins and automatically imposes the conservation of boundary currents. This new construction is formulated in twistor space, a complex projective space that encodes solutions to equations of motion as holomorphic data. This is done via an isomorphism called the Penrose transform. First, I will discuss the case of AdS_3 and AdS_5, where bulk-to-boundary correlators naturally arise in minitwistor space. Then, I will show how in (A)dS₄ one can construct bulk correlation functions using only twistors, dual twistors, and the infinity twistor as building blocks. The relation to coordinate space arises now via nested Penrose transforms. The boundary limit of these correlators yields CFT correlators/wavefunction coefficients that satisfy the expected Ward identities. Finally, I will briefly discuss how this can be generalized to AdS_5 boundary correlators using ambitwistors.
