As an organizer of the microtubule cytoskeleton in animals, the centrosome has an important function. From the early light microscopic observation of the centrosome to examination by electron microscopy, the centrosome field is now in an era of molecular identification and precise functional analyses. Tables compiling centrosomal proteins and reviews on the centrosome are presented here and demonstrate how active the field is. However, despite this intense research activity, many classical questions are still unanswered. These include those regarding the precise function of centrioles, the mechanism of centrosome duplication and assembly, the origin of the centrosome, and the regulation and mechanism of the centrosomal microtubule nucleation activity. Fortunately, these questions are becoming elucidated based on experimental data discussed here. Given the fact that the centrosome is primarily a site of microtubule nucleation, special focus is placed on the process of microtubule nucleation and on the regulation of centrosomal microtubule nucleation capacity during the cell cycle and in some tissues.