Abstract： Engineering of domains and domain boundaries is quintessential for technological exploitation of numerous functional materials. However, it has only recently realized that the configurations of these domains/domain walls with 2D-vector vorticity can have non-trivial topology, and these topological vortex domains are rather universal, unless long-range interaction such as ferroelastic coupling or dipolar coupling dominates. We have also found vortex-like domain configurations, which have vorticity in energy diagram, but not in real space, and are called pseudo-vortex domains. We will discuss the difference between these two types of domain configurations in a number of quantum materials, especially with coexisting multiple orders of charge/spin/lattice degrees of freedom.