  Superfluid vortices are quantum excitations carrying quantized amount of
orbital angular momentum in a phase where global symmetry is spontaneously
broken. We address a question of whether magnetic vortices in superconductors
with dynamical gauge fields can carry nonzero orbital angular momentum or not.
We discuss the angular momentum conservation in several distinct classes of
examples from crossdisciplinary fields of physics across condensed matter,
dense nuclear systems, and cosmology. The angular momentum carried by gauge
field configurations around the magnetic vortex plays a crucial role in
satisfying the principle of the conservation law. Based on various ways how the
angular momentum conservation is realized, we provide a general scheme of
classifying magnetic vortices in different phases of matter.
