Photorefractive volume holography for processing ultrashort optical pulses carrying spatial, temporal, and spatiotemporal optical information is introduced. These new holographic methods can process temporal information, i.e., the temporal evolution of optical pulse signals, in addition to the usual spatial information. Photorefractive volume holographic materials provide the medium necessary for recording and reconstruction of such optical information in real time. Spatial and temporal holography with photorefractive volume holographic materials are introduced, compared, and discussed. The direct time-domain holography is shown to possess two disadvantages, low fringe contrast and limited recording time, which is overcome by using the method of spectral domain holography. Applications of direct time-domain and spectral-domain holography for image processing, temporal matched filtering, optical pulse shaping, three-dimensional (3-D) optical storage, and optical interconnects are discussed. Furthermore, the combined space-time holographic processing that allows the conversion between the spatial and the temporal optical information carrying channels is introduced. This method is used to demonstrate experimentally parallel-to-serial and serial-to-parallel data conversion for one-dimensional (1-D) images and image-format data transmission. The demonstrated holographic processors provide the advantages of self-referenced signal transmission and self-compensation for optical dispersion induced by the holographic materials, communication channel, as well as other optical components.