  The Event Horizon Telescope (EHT) Collaboration has successfully produced
images of two supermassive black holes, enabling novel tests of black holes and
their accretion flows on horizon scales. The EHT has so far published total
intensity and linear polarization images, while upcoming images may include
circular polarization, rotation measure, and spectral index, each of which
reveals different aspects of the plasma and space-time. The next-generation EHT
(ngEHT) will greatly enhance these studies through wider recorded bandwidths
and additional stations, leading to greater signal-to-noise, orders of
magnitude improvement in dynamic range, multi-frequency observations, and
horizon-scale movies. In this paper, we review how each of these different
observables informs us about the underlying properties of the plasma and the
spacetime, and we discuss why polarimetric studies are well-suited to
measurements with sparse, long-baseline coverage.
