This paper addresses the effects of domain boundaries on the behaviour of quasi-two-dimensional flows, thereby distinguishing between lateral boundaries of horizontal flow domains and the horizontal boundaries confining shallow fluid layers. As already discussed in some recent papers, the lateral walls may play an essential role in acting as sources of filamentary high-amplitude vorticity, which usually affects the flow evolution in the interior of the domain. Besides, walls exert forces that may promote the self-organization of the flow, and hence contribute to a change in the net angular momentum of the flow. Both aspects will be reviewed briefly. In contrast to what is commonly assumed, shallow-layer flows may develop an essentially three-dimensional structure, with vertical gradients in the principal horizontal flow field and with significant vertical velocity components. These features have been found recently in experiments on electromagnetically generated flows in a shallow fluid layer. In this paper, we will discuss some of these experimental observations as well as some numerical simulation results that are helpful in explaining the observed flow dynamics. © 2009 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.