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We present a review of quantum computation with neutral atom qubits. After an overview of architectural options and approaches to preparing large qubit arrays we examine Rydberg mediated gate protocols and fidelity for two-and multi-qubit interactions. Quantum simulation and Rydberg dressing are alternatives to circuit based quantum computing for exploring many body quantum dynamics. We review the properties of the dressing interaction and provide a quantitative figure of merit for the complexity of the coherent dynamics that can be accessed with dressing. We conclude with a summary of the current status and an outlook for future progress.