Translucency is an optical and a perceptual phenomenon that characterizes subsurface light transport through objects and materials. Translucency as an optical property of a material relates to the radiative transfer inside and through this medium, and translucency as a perceptual phenomenon describes the visual sensation experienced by humans when observing a given material under given conditions. The knowledge about the visual mechanisms of the translucency perception remains limited. Accurate prediction of the appearance of the translucent objects can have a significant commercial impact in the fields such as three-dimensional printing. However, little is known how the optical properties of a material relate to a perception evoked in humans. This article overviews the knowledge status about the visual perception of translucency and highlights the applications of the translucency perception research. Furthermore, this review summarizes current knowledge gaps, fundamental challenges and existing ambiguities with a goal to facilitate translucency perception research in the future.