  Over half a century from the discovery of gamma-ray bursts (GRBs), the
dominant radiation mechanism responsible for their bright and highly variable
prompt emission remains poorly understood. Spectral information alone has
proven insufficient for understanding the composition and main energy
dissipation mechanism in GRB jets. High-sensitivity polarimetric observations
from upcoming instruments in this decade may help answer such key questions in
GRB physics. This article reviews the current status of prompt GRB polarization
measurements and provides comprehensive predictions from theoretical models. A
concise overview of the fundamental questions in prompt GRB physics is
provided. Important developments in gamma-ray polarimetry including a critical
overview of different past instruments are presented. Theoretical predictions
for different radiation mechanisms and jet structures are confronted with
time-integrated and time-resolved measurements. The current status and
capabilities of upcoming instruments regarding the prompt emission are
presented. The very complimentary information that can be obtained from
polarimetry of X-ray flares as well as reverse-shock and early to late
forward-shock (afterglow) emission is highlighted. Finally, promising
directions for overcoming the inherent difficulties in obtaining statistically
significant prompt-GRB polarization measurements are discussed, along with
prospects for improvements in the theoretical modeling, which may lead to
significant advances in the field.
