This talk reviews recent theoretical and experimental findings on the open-system dynamics of entanglement, which can differ in remarkable ways from the dynamics of the individual components of the system. Decoherence leads to non-exponential decay of entanglement, which may vanish even when coherence is still present in the system. These results, which have been recently probed by quantum optics experiments, are relevant for assessing the robustness of applications like quantum communication and computation, as well as for addressing fundamental questions, already raised by Einstein and Schrodinger, concerning the classical limit of quantum mechanics.