Abstract: I will discuss recent and ongoing work with Emil Have, Stefan Prohazka and Jakob Salzer on possible kinematics for flat space holography.  I will discuss how a seemingly novel projective compactification of Minkowski spacetime reveals a rich asymptotic geometry homogeneous under the Poincaré group and including the blow-ups at spatial and timelike infinities as well as a novel four-dimensional space intimately associated to null infinity.  This allows for novel geometric descriptions of the Minkowski asymptotic geometries and gives us a glimpse of the asymptotic geometry of asymptotically flat spaces.