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An essential task in the celestial holography program which seeks to find a holographic principle for asymptotically flat spacetimes is the identification of the symmetries which must govern both sides of any holographically dual pair. A concerted effort over the past few years has revealed that the infrared structure of gauge theory and gravity encodes the symmetries of a celestial conformal field theory that lives on the sphere at the null boundary of asymptotically flat spacetimes. In this talk I will explain how soft limits in quantum field theory combined with powerful CFT tools allow us to classify the soft symmetries of celestial CFT in general d dimensions.