Cell migration requires polarization of the cell into the leading edge and the trailing edge. Microtubules (MTs) are indispensable for polarized cell migration in the majority of cell types. To support cell polarity, MT network has to be functionally and structurally asymmetric. How is this asymmetry achieved? In interphase cells, MTs form a dynamic system radiating from a centrosome-based MT-organizing center (MTOC) to the cell edges. Symmetry of this radial array can be broken according to four general principles. Asymmetry occurs due to differential modulation of MT dynamics, relocation of existing MTs within a cell, adding an asymmetric nucleation site, and/or repositioning of a symmetric nucleation site to one side of a cell. Combinations of these asymmetry regulation principles result in a variety of asymmetric MT networks typical for diverse motile cell types. Importantly, an asymmetric MT array is formed at a non-conventional MT nucleation site, the Golgi. Here, we emphasize the contribution of this array to the asymmetry of MT network.