  We summarize the current state of polarization observations of Sagittarius
A*, the compact radio source and supermassive black hole candidate in the
Galactic Center. These observations are providing new tools for understanding
accretion disks, jets and their environments. Linear polarization observations
have shown that Sgr A* is unpolarized at frequencies as high as 86 GHz.
However, recent single-dish observations indicate that Sgr A* may have strong
linear polarization at frequencies higher than 150 GHz. Circular polarization,
which was recently discovered in Sgr A*, is detectable to frequencies as high
as 43 GHz. It is strongly variable on a 10-day timescale, with the degree of
variability increasing with frequency. At low frequencies, fractional circular
polarization is stable over nearly 20 years. We discuss some of the possible
models for the origin of the circular polarization.
