The microtubule network dictates much of the spatial patterning of the cytoplasm, and the coupling of microtubules to membranes controls the structure and positioning of organelles and directs membrane trafficking between them. The connection between membranes and the microtubule cytoskeleton, and the way in which organelles are shaped and moved by interactions with the cytoskeleton, have been studied intensively in recent years. In particular, recent work has expanded our thinking of this topic to include the mechanisms by which membranes are shaped and how cargo is selected for trafficking as a result of coupling to the cytoskeleton. In this Commentary, I will discuss the molecular basis for membrane–motor coupling and the physiological outcomes of this coupling, including the way in which microtubule-based motors affect membrane structure, cargo sorting and vectorial trafficking between organelles. Whereas many core concepts of these processes are now well understood, key questions remain about how the coupling of motors to membranes is established and controlled, about the regulation of cargo and/or motor loading and about the control of directionality.