Bigraph was proposed by Robin Milner in 2001 as a formal theoretical model based on graphs in attempt to provide a design, simulation and analysis platform for ubiquitous computing and present a unified, extensible framework for the existing process algebra. In this paper first introduces the basic concepts of bigraph and reveals relationships among precategory, category, s-category and symmetric partial monoidal category which form the mathematical basis of bigraph, and then summarizes bigraphical algebra system while providing a simplified representation of the discrete normal form in bigraph with a proof. Next, it discusses some questions related to the definition of bigraphical categories and quotient translations after making a survey of the development of bigraph and its applications. This study argues that bigraphical category should be small category other than large category. Moreover, the paper illustrates how to convert the large category derived by quotient to small category. Finally, it outlines the extensions of bigraphical models and their applications.