The analysis of compact astronomical objects has generally dealt with the physical properties of the source within a two-parameter space, which is defined by the spectral characteristics and time variability. This approach often leads to the situation whereby two or-more very differ ent models can explain the observations successfully. Polarimetric observations have the diagnostic potential to discriminate between the different compact source models and can offer a unique insight into the geometrical nature of the emission zones. To date, however, no polarization observation in the gamma-ray energy domain has been successfully performed, due to the difficulties in making polarimetric measurements in this high-energy region of the spectrum. In this piper the polarized gamma-ray emission mechanisms are reviewed with the emphasis on their detectable characteristics. Potential astronomical sites in which these emission mechanisms may be at work are discussed. Observational results obtained in other wavebands and theoretical predications made for some of the most likely astronomical sources of polarization are reviewed. Compton polarimetry has long been used in the field of nuclear gamma-ray spectroscopy in the laboratory. The operational principle behind all generations of nuclear gamma-ray polarimeters has been to measure the asymmetry in the azimuthal distribution of the scattered photons. However none of the polarimeters designed for laboratory experiments will be sensitive enough to observe even the strongest astronomical source. In the past few years there have been a number of innovative developments aimed at the construction of astronomical gamma-ray polarimeters, either as dedicated experiments or in missions with polarimetric capability. The designs of all the polarimeters are based on either discrete or continuous position sensitive detector planes. In this paper the data analysis techniques associated with this type of polarimeter are discussed as well as methods of removing some of the systematic effects introduced by a non-ideal detector response function and observation conditions. Laboratory tests of these new polarimetric techniques are reviewed. They demonstrate the feasibility of building a suitably sensitive astronomical gamma-ray polarimeter. Optimization of the design of pixellated detector an ay based polarimeters is also addressed. The INTEGRAL mission, which is to be launched by ESA in the year 2001, is the most likely telescope to perform the first successful gamma-ray polarization observation. The polarimetric characteristics of the two main instruments on board INTEGRAL are evaluated and their sensitivities to a wide range of potentially polarized gamma-ray sources are estimated.
