  Ongoing millimeter VLBI observations with the Event Horizon Telescope allow
unprecedented study of the innermost portion of black hole accretion flows.
Interpreting the observations requires relativistic, time-dependent physical
modeling. We discuss the comparison of radiative transfer calculations from
general relativistic MHD simulations of Sagittarius A* and M87 with current and
future mm-VLBI observations. This comparison allows estimates of the viewing
geometry and physical conditions of the Sgr A* accretion flow. The viewing
geometry for M87 is already constrained from observations of its large-scale
jet, but, unlike Sgr A*, there is no consensus for its millimeter emission
geometry or electron population. Despite this uncertainty, as long as the
emission region is compact, robust predictions for the size of its jet
launching region can be made. For both sources, the black hole shadow may be
detected with future observations including ALMA and/or the LMT, which would
constitute the first direct evidence for a black hole event horizon.
