This thesis investigates quantum storage in europium-doped yttrium orthosilicate using the atomic frequency comb protocol. It is studied how a small magnetic bias field affects the various aspects of the storage protocol. The application of such a bias field in combination with dynamical decoupling techniques is demonstrated to increase the coherence time of classical storage by more than two orders of magnitude to up to 0.5 s. Further, time-bin qubit storage for up to 20 ms is demonstrated. In the context of these storage experiments, dynamical decoupling from spectral diffusion that is described an Ornstein-Uhlenbeck process is studied in detail. Finally, a novel approach for quantum memory-assisted time-bin qutrit projection is proposed and implemented in a storage experiment with bright pulses and studied within a full Maxwell-Bloch simulation.