This review summarizes the data describing the role of cellular microtubules in transportation of membrane vesicles - transport containers for secreted proteins or lipids. Most events of early vesicular transport in animal cells (from the endoplasmic reticulum to the Golgi apparatus and in the opposite recycling direction) are mediated by microtubules and microtubule motor proteins. Data on the role of dynein and kinesin in early vesicle transport remain controversial, probably because of the differentiated role of these proteins in the movements of vesicles or membrane tubules with various cargos and at different stages of secretion and retrograde transport. Microtubules and dynein motor protein are essential for maintaining a compact structure of the Golgi apparatus; moreover, there is a set of proteins that are essential for Golgi compactness. Dispersion of ribbon-like Golgi often occurs under physiological conditions in interphase cells. Golgi is localized in the leading part of crawling cultured fibroblasts, which also depends on microtubules and dynein. The Golgi apparatus creates its own system of microtubules by attracting γ-tubulin and some microtubule-associated proteins to membranes. Molecular mechanisms of binding microtubule-associated and motor proteins to membranes are very diverse, suggesting the possibility of regulation of Golgi interaction with microtubules during cell differentiation. To illustrate some statements, we present our own data showing that the cluster of vesicles induced by expression of constitutively active GTPase Sar1a[H79G] in cells is dispersed throughout the cell after microtubule disruption. Movement of vesicles in cells containing the intermediate compartment protein ERGIC53/LMANI was inhibited by inhibiting dynein. Inhibiting protein kinase LOSK/SLK prevented orientation of Golgi to the leading part of crawling cells, but the activity of dynein was not inhibited according to data on the movement of ERGIC53/LMANI-marked vesicles.