<p>We briefly review the current status of magnetogenesis, a cross-disciplinary field bridging cosmology and plasma physics to study the origin of magnetic fields in the universe. We adopt the canonical vorticity framework to investigate kinetic magnetogenesis processes in collisionless plasmas. By considering canonical vorticity, a weighted sum of the fluid vorticity and magnetic field as the canonical variable, this framework unifies diverse magnetogenesis processes as manifestations of the general pressure tensorial configurations named as canonical battery effect. This unified well-known processes like the Biermann battery and Weibel instability, while predicting several new pressure tensorial configurations as the fundamental source of self-generated magnetic field and vorticity in plasma. The framework is further extended to a relativistic regime where an additional source of canonical vorticity, named the kineclinicity effect, is identified. These theoretical predictions are systematically validated through particle-in-cell (PIC) simulations, highlighting their implications in laboratory and astrophysical plasma environments.</p>