Synthetic hectorite clay Laponite RD/XLG is composed of disk-shaped nanoparticles that acquire dissimilar charges when suspended in an aqueous media. Owing to their property to spontaneously self-assemble, Laponite is used as a rheology modifier in a variety of commercial water-based products. Particularly, aqueous dispersion of Laponite undergoes liquid - to - solid transition at about 1 volume % concentration. The evolution of the physical properties as dispersion transforms to solid state is reminiscent of physical aging in molecular as well as colloidal glasses. The corresponding soft glassy dynamics of an aqueous Laponite dispersion, including the rheological behavior, has been extensively studied in the literature. In this feature article we take an overview of recent advances in understanding soft glassy dynamics and various efforts taken to understand the peculiar rheological behaviors. Furthermore, the continuously developing microstructure that is responsible for eventual formation of soft solid state that supports its own weight against gravity has also been a topic of intense debate and discussion. Particularly extensive experimental and theoretical studies lead to two types of microstructures for this system: an attractive gel-like or repulsive glass like. We carefully examine and critically analyze the literature and propose a state diagram that suggests aqueous Laponite dispersion to be present in an attractive gel state.