  We examine the BCFW recursion relations for celestial amplitudes and how they
inform the celestial bootstrap program. 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: $z\to
\infty$ and $z\to 0$. 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. The extension to super-BCFW is also
presented. We close by remarking on several open questions for future study.

High Energy Physics - Theory