Various industries, e. g., manufacturers of optical components or medical equipment, use components made out of transparent materials to craft devices for high-precision applications. As this involves the need for fulfilling high quality assurances, any kind of defect like enclosed air bubbles, contaminants or cracks, has to be reliably detected. Much effort has been spent and is currently spent into developing methods suitable for visually inspecting transparent objects. In contrast to opaque objects, transparent materials pose various challenging problems, as any light ray involved in the inspection process can be reflected and refracted by the investigated sample, complicating the design of the setup and of the method used for the inspection. On the one hand, this report gives an introduction to the specific physical properties of interest of transparent objects. On the other hand, it provides an overview over existing methods used for capturing these properties and describes sketches of some novel inspection approaches.