Upcoming VLBI observations will resolve nearby supermassive black holes, most notably Sagittarius A* and M87, on event horizon-scales. Recent observations of Sagittarius A* with the Event Horizon Telescope have revealed horizon-scale structure. Accordingly, the detection and measurement of the back hole “shadow” is expected to enable the existence of astrophysical black holes to be verified directly. Although the theoretical description of the shadow is straightforward, its observational appearance is largely determined by the properties of the surrounding accretion flow, which is highly turbulent. We introduce a new polarised general-relativistic radiative transfer code, BHOSS, which accurately solves the equations of polarised radiative transfer in arbitrary strong-gravity environments, providing physically-realistic images of astrophysical black holes on event horizon-scales, as well as also providing insight into the fundamental properties and nature of the surrounding accretion flow environment.