A review of the role of the microtubule motor dynein and its cofactor dynactin in the formation of a radial system of microtubules in the interphase cells and of mitotic spindle. Deciphering of the structure, functions, and regulation of activity of dynein and dynactin promoted the understanding of mechanisms of cell and tissue morphogenesis, since it turned out that these cells help the cell in finding its center and organize microtubule-determined anisotropy of intracellular space. The structure of dynein and dynactin molecules has been considered, as well as possible pathways of regulation of the dynein activity and the role of dynein in transport of cell components along the microtubules. Attention has also been paid to the functions of dynein and dynactin not related directly to transport: their involvement in the formation of an interphase radial system of microtubules. This system can be formed by self-organization of microtubules and dynein-containing organelles or via organization of microtubules by the centrosome, whose functioning requires dynein. In addition, dynein and dynactin are responsible for cell polarization during its movement, as well as for the position of nucleus, centrosomes, and mitotic spindle in the cell.