  General-relativistic radiative transfer (GRRT) calculations coupled with the
calculation of geodesics in the Kerr spacetime are an essential tool for
determining the images, spectra and light curves from matter in the vicinity of
black holes. Such studies are especially important for ongoing and upcoming
millimeter/submillimeter (mm/sub-mm) Very Long Baseline Interferometry (VLBI)
observations of the supermassive black holes at the centres of Sgr A^{*} and
M87. To this end we introduce Odyssey, a Graphics Processing Unit(GPU)-based
code for ray tracing and radiative transfer in the Kerr spacetime. On a single
GPU, the performance of Odyssey can exceed 1 nanosecond per photon, per
Runge-Kutta integration step. Odyssey is publicly available, fast, accurate,
and flexible enough to be modified to suit the specific needs of new users.
Along with a Graphical User Interface (GUI) powered by a video-accelerated
display architecture, we also present an educational software tool,
Odyssey_Edu, for showing in real time how null geodesics around a Kerr black
hole vary as a function of black hole spin and angle of incidence onto the
black hole.
