Referenceless phase holography (RELPH) is a lensless holographic method that generates the full (amplitude and phase) optical field if intensity and phase distributions of this field in one plane are given as numerical data. It is based on the interference of two pure phase fields that are produced by reflection of two mutually coherent plane waves at two phase modulating spatial light modulators (SLM). The optical field of any real or artificial three-dimensional (3D) scene can be displayed. This means that referenceless phase holography is a promising method for future 3D television or 3D cinema as well as for interferometric metrology. We introduce the theory of RELPH, possible technical realizations, and discuss the numerics. The possibilities and problems in calculating the diffraction fields of given 3D scenes are worked out, modifications of the algorithms are presented. Experiments are shown, not only proving the practicability of RELPH, but also confirming the various 3D cues, such as depth of field, occlusion, and parallax. Two approaches to multicolor display are presented and experimentally verified. The benefits and advantages of RELPH are outlined, open problems and necessary technological developments as well as possibilities and future prospects are discussed.