In computer graphic (CG), illumination rendering generated realistic effect at virtual scene is amazing. Not only plausible lighting effect is to show the relative position between of the objects, but also to reflect the material of visual appearance of the vir- tual objects. The diffuse-scene rendering reflectance credibility has gradually matured. Global illumination rendering method for the glossy material is still a challenge for the CG research. Because of the shiny materials is highly energy reflection between the com- plex light paths. Whether we trace glossy reflection paths, or use of one-reflection or multi-reflection approximate above complex il- lumination transmission is a difficult working. This paper we gather some commonly used global illumination algorithms recently year and its extension glossy scene improvements. And we introduce the limitation of classical algorithms rendering glossy scene and some extended solution. Finally, we will summarize the illumination rendering for specular scene, there are still some open prob- lems.