Black holes are among the most celebrated predictions of Einstein’s general theory of relativity. The mathematical study of black hole dynamics is a problem of fundamental importance with far-reaching implications, for instance for the cosmic censorship conjecture and gravitational wave propagation. Despite tremendous progress on subextremal black holes, many challenges remain in the extremal limit. The present thesis investigates the dynamics of the exterior of the Reissner-Nordström black hole through the lens of the massless Vlasov equation. We place particular emphasis on contrasting the dynamical properties of the subextremal and the extremal Reissner-Nordström solution. We prove that moments of the massless Vlasov equation decay pointwise at an exponential rate in the subextremal case and at a polynomial rate in the extremal case. This polynomial rate is shown to be sharp along the event horizon. In the extremal case we show that transversal derivatives of certain components of the energy-momentum tensor do not decay along the event horizon if the solution and its first time derivative are initially supported on the event horizon. The non-decay of transversal derivatives in the extremal case is compared to the classical work of Aretakis on instability for the wave equation. In contrast to Aretakis’ results, the present work does not rely on conservation laws. Our proof is based entirely on a quantitative analysis of the geodesic flow. In addition, using only minimal information about the geodesic flow, we can already show quadratic decay of energy with a much simpler method of proof. By adapting classical techniques from the wave equation, we establish in particular a non-degenerate Morawetz estimate for the massless Vlasov equation with only an ‘ε-loss of regularity in the trapping directions’.