The centrosome, which consists of two centrioles surrounded by pericentriolar material, is a unique structure that has retained its main features in organisms of various taxonomic groups from unicellular algae to mammals over one billion years of evolution. In addition to the most noticeable function of organizing the microtubule system in mitosis and interphase, the centrosome performs many other cell functions. In particular, centrioles are the basis for the formation of sensitive primary cilia and motile cilia and flagella. Another principal function of centrosomes is the concentration in one place of regulatory proteins responsible for the cell’s progression along the cell cycle. Despite the existing exceptions, the functioning of the centrosome is subject to general principles, which are discussed in this review.