Quantum information uses special properties of quantum systems to manipulate or transmit data. This results in new processes, which are impossible to obtain with classical devices. For example, quantum computing and quantum storage, which are two important fields in quantum information research, aim respectively at performing very fast calculations and at storing quantum states of photons. These two applications could be obtained in solid-state systems using rare earth doped crystals. In this context, the most important property of these materials is the long coherence lifetimes of rare earth ion optical and hyperfine transitions. This allows one to create long-lived superposition states, which is a fundamental requirement for efficient quantum computing and storage. Promising results have already been demonstrated in rare earth doped crystals but it will be difficult to improve them with current materials. In this paper, we discuss the general and specific requirements for rare earth ions and crystals in order to perform quantum computing with a large number of quantum bits as well as all solid-state quantum storage. We also present the properties of a few recently studied crystals: Ho3+:YVO4, Ho3+:LuVO4 (quantum computing) and Tm3+:Y3Al5O12 (quantum storage).