Topological spin textures, such as domain walls in one dimension, vortices in two dimensions and magnetic hedgehogs in three dimensions, are promising candidates for nonlocal transport due to their stability against local fluctuations. They follow general topological conservation laws, based on which hydrodynamic theories can be formulated. In this talk, I will introduce the physical principles to drive, transport, and detect topological spin textures, and explain them with experimentally viable proposals. In particular, I will talk about a promising all-spin hardware implementation of neuromorphic computing utilizing domain walls in quasi-one-dimensional antiferromagnets; an energy-storage proposal based on free energy stored in winding textures, which can be controlled via the vorticity flow; and a scheme for three-dimensional nonlocal transport of magnetic hedgehogs. If time permits, I will briefly discuss an electrodynamic view of the XY and Heisenberg ferromagnets.