[en] Highlights: • General theory for angle and spin dependence of dichroic core-level photoemission. • Fundamental spectra give correlation between spin and orbital moments. • Interference term between emission channels results in MLDAD and CDAD. • Core-hole polarization is probed by resonant photoemission. - Abstract: The discovery of magnetic dichroism in photoemission is celebrating its 25th anniversary this year. Here a review of the underlying general theory for the angular and spin dependence of dichroic core-level photoemission is presented using both a single-particle model and a many-body approach. The established methods of angular momentum coupling offer an elegant and powerful way to analyse the magnetic dichroism and spin polarization in photoemission from core and localized valence levels. In the presence of core-valence interactions one can distinguish different fundamental spectra, which via sum rules are related to physical properties described by coupled tensor operators for spin and orbital moments. By separating the angular dependence from the physical information, different geometries can be distinguished to measure the magnetic circular dichroism (MCD), linear dichroism (LD), circular dichroism in the angular dependence (CDAD), and magnetic linear dichroism in the angular dependence (MLDAD). Various ways to probe the core-hole polarization are discussed, such as using the angular dependence, moment analysis of the spectral distribution, and resonant photoemission decay.