In holographic spectroscopy an image of an interference pattern is pro
jected onto a detector and transformed back to the input spectrum. The
general characteristics are similar to those of Fourier transform spe
ctroscopy, but the spectrum is obtained without scanning. In the heter
odyned arrangement one or more diffraction gratings are used so that h
igh-resolution spectra can be recorded without a corresponding increas
e in the recording density. The technique offers interesting possibili
ties, but is not without difficulties. The purpose of this paper is to
review recent developments, especially in astronomical applications,
to describe the theoretical background to typical problems such as coh
erence losses, and to discuss the extent to which these can be solved
in practical instrumentation.