I will discuss recent progress on understanding and harnessing collective transport in magnetic insulators. Central to this talk will be conservation laws that are rooted in a topological invariant rather than a global symmetry. In one example, the emergent hydrodynamics closely mimics neutral superfluidity, which may allow to establish and utilize superflows in solid-state devices at room temperature. Other examples will include magnetic films harboring skyrmionic textures and, surprisingly, disordered glassy spin systems. Recently developed magnetoelectric and thermoelectric techniques are now allowing us to systematically access this physics in a range of materials, both old and new.