When electrons move in a magnetic material, their transport can be profoundly affected by scattering off magnetic ions. Converse is also true: Itinerant electrons themselves can define the magnetic state into which the system orders. Even though typically these magnetic states are simple ' e.g. ferromagnetic or antiferromagnetic ' sometimes, complex chiral magnetism can appear. In this talk I will present several examples of two- and three-dimensional itinerant models of magnetism that exhibit complex non-coplanar ordering even in the absence of spin orbit interaction; I will describe possible material realizations. Non-coplanar itinerant magnets are expected to exhibit highly unusual transport phenomena that stem from a quantum coherent effect of non-coplanar magnetic ordering on electrons, which is similar to the Aharonov-Bohm effect. It can lead to the spontaneous quantum Hall effect and ground-state electrical and spin currents. The equivalent strength of the orbital magnetic field can exceed 10^4 Tesla. The stable topological excitations (magnetic vortices) in these states can carry fractional electronic charge and spin and realize anyonic exchange statistics.