Motivated by the extension of the AdS/CFT correspondence to asymptotically flat space-times and in particular the Carrollian approach to flat-space holography, I will present a holographic realisation of conformal (massless) Carrollian scalar field theories, seen as boundary degrees of freedom living on the null infinity of Minkowski space-time. I will present both the electric and magnetic theories, with a particular emphasis on their symmetries. This analysis may serve as a first step towards establishing a holographic dictionary, and I will argue that both theories are crucial in the study of flat-space higher-spin holography.