  Massless scattering amplitudes in four-dimensional Minkowski spacetime can be
Mellin transformed to correlation functions on the celestial sphere at null
infinity called celestial amplitudes. We study various properties of massless
four-point scalar and gluon celestial amplitudes such as conformal partial wave
decomposition, crossing relations and optical theorem. As a byproduct, we
derive the analog of the single and double soft limits for all gluon celestial
amplitudes.
