In this talk, I will begin with a brief introduction to celestial holography and setting up the celestial amplitudes, before diving into some recent results on examining the BCFW recursion relations for celestial amplitudes. We start by recasting the celestial incarnation of the BCFW shift as a generalization of the action of familiar asymptotic symmetries on hard particles, before focusing on two limits: large-z and infinitesimal-z. We then discuss how the celestial CFT data encodes the large-z behavior determining which shifts are allowed, while the infinitesimal limit is tied to the celestial bootstrap program via the BG equations that constrain the MHV sector.
