  We theoretically investigate cooperative effects in cold atomic gases
exhibiting both electric and magnetic dipole-dipole interactions, such as
occurring for example in clouds of dysprosium atoms. We distinguish between the
quantum degenerate case, where we take a many body physics approach and the
quantum non-degenerate case, where we use the formalism of open system
dynamics. For quantum non-degenerate gases, we illustrate the emergence of
tailorable spin models in the high-excitation limit. In the low-excitation
limit, we provide analytical and numerical results detailing the effect of
magnetic interactions on the directionality of scattered light and characterize
sub- and superradiant effects. For quantum degenerate gases, we study the
interplay between sub- and superradiance effects and the fermionic or bosonic
quantum statistics nature of the ensemble.
