A holographic volumetric display comprises a pattern generation unit (20), a programmable lighting device and a holographic screen (28). The holographic screen contains one or more pre-recorded set(s) of spatially sampled holographic interference patterns (or sub-holograms) each capable of reproducing one or more volume element(s) or voxel(s) (32) in three dimensional space outside the plane of the holographic screen when each sub-hologram is selectively illuminated. A sub-hologram is a sampled hologram of a voxel and sub-holograms in one set are spatially interleaved across the surface of the holographic screen with other sub-holograms. The programmable lighting device may be provided by a color digital projection unit (28) and the pattern generation unit which can illuminate any number of sub-holograms on the holographic screen. In this way, a volumetric display with holographic voxels can be made. The holographic volumetric display can reconstruct three-dimensional moving images in color.