The aim of this report is firstly to review colour display holography and secondly to present some of the work carried out in our laboratories in this field, An historical introduction is presented, setting out key events in the development of colour holography, and several historical parallels are drawn with colour photography. Laser illuminated colour holography and its problems, in particular that of spurious images is discussed. White-light-viewable colour holograms are divided into reflection, rainbow and dispersion-compensated types. The latter is a description of recent experiments by us. Colour rendition in holographic images is discussed. It is concluded that improvements in panchromatic photographic emulsions, and development of inexpensive lasers operating at or near 450, 540 and 610 nm may be the most important future developments for colour holography.