Recent studies suggest that important contributions to the CME originate in the pre-equilibrium phase of a collision. While real-time lattice simulations can be utilized to understand the dynamics of anomalous effects in the earliest stages of a collision, quantitative predictions of experimental signatures are only feasible once the subsequent transport of the messengers of the CME through the fireball are understood. This motivates the need of a Chiral Kinetic Theory for relativistic fermions. In this talk we present a novel approach based on the world line formulation of quantum field theory that clarifies the relative role of a possible Berry phase and chiral anomaly that generates topological transitions. Our formulation is Lorentz covariant and independent of adiabatic approximations. Employing a coarse graining procedure, we derive a Chiral Boltzmann equation with collision terms. Our framework allows us to follow ab initio the fate of the Chiral Magnetic current from the earliest times (via solutions of the Dirac equation in topological sphaleron backgrounds) through its matching to Chiral Kinetic Theory and finally to Chiral MagnetoHydrodynamics. We discuss the implications of our results for quantitative extraction of the CME in heavy-ion collisions.