SUMMARYHolography can be used to record, on a flat photographic plate, information about a three‐dimensional object. In conventional microscopy a thin slice of an object is observed in focus and recorded. By combining microscopy and holography it is possible to encode, on the same flat record, all the depth information in a three‐dimensional microscopic object, not just a single infocus section. Any section of the three‐dimensional object may be subsequently reconstructed and brought into focus by using a suitable viewing system to decode the hologram. Arrangements for doing this are described. It is shown that in order to achieve the highest resolution imagery of a three‐dimensional object, reversed wave reconstruction is necessary.As holograms are made and reconstructed using a coherent laser light source, holographic microscopes are easily adapted for interferometry and an example of this is described. The differences between coherent and conventional imagery are briefly considered. The coherence of the illumination gives rise to the problems of coherent noise and speckle. Coherent noise is due to stray reflections in the optical system and can be reduced by using as few surfaces as possible or by using holographic lenses. A speckle reduction technique employing a new type of holographic optical element is described and its application to the stereomicroscopy of fossil ostracods con