Drifting, or cornering with rear tires that exceed slip limits, represents a trade-off of stability for controllability while operating at the limits of friction. Recent work has demonstrated exceptional performance by autonomous systems of stabilization and path tracking a vehicle around an unstable drifting equilibrium. However, safely navigating unexpected or challenging road conditions that require an autonomous vehicle to operate at the limits of friction is likely to require dynamic, nonequilibrium maneuvers. These trajectories activate underlying dynamics, such as weight transfer and wheelspeed, which significantly affect the forces acting on the vehicle. In this paper, we present a modeling and control framework for dynamic drifting trajectories. First, a novel vehicle model is proposed that strikes an appropriate balance of fidelity and complexity. Then, this vehicle model is embedded into a Nonlinear Model Predictive Control policy that can maintain stability and path tracking while performing dynamic drifting maneuvers. This work is validated experimentally using "Takumi", an autonomous Toyota Supra, that demonstrates root mean squared path tracking error of 13 centimeters and a peak error of just 47 cm. Finally, a simulation study suggests parameter uncertainty, rather than additional model fidelity, is the primary limitation of further increasing controller performance.