A specialized region of all eukaryote cells except fungi, situated next to the nucleus, that organizes the microtubules of the spindle during cell division. It also serves as the chief microtubule-organizing centre in animal cells. The centrosomes of most animal cells contain a pair of centrioles. During metaphase of mitosis and meiosis, the centrosome separates into two regions, each containing one of the centrioles (where present). The two regions move to opposite ends of the cell and a spindle forms between them.