While the scientific potential of high-energy X-ray and gamma-ray polarimetry
has long been recognized, measuring the polarization of high-energy photons is
challenging. To date, there has been very few significant detections from an
astrophysical source. However, recent technological developments raise the
possibility that this may change in the not-too-distant future. Significant
progress has been made in the development of Gamma-ray Burst (GRB) polarimeters
and polarization sensitive Compton telescopes. A second-generation dedicated
GRB polarimeter, POLAR-2, is under development for launch in 2024, and COSI a
second-generation polarization sensitive Compton Telescope has been selected by
NASA for launch in 2025. This chapter reviews basic concepts and experimental
approaches of scattering polarimetry of hard X-rays to MeV {\gamma}-rays, and
pair production polarimetry of higher-energy photons
