Quantum information can be processed using large ensembles of ultracold and trapped neutral atoms, building naturally on the techniques developed for high-precision spectroscopy and metrology. This article reviews some of the most important protocols for universal quantum logic with trapped neutrals, as well as the history and state-of-the-art of experimental work to implement these in the laboratory. Some general observations are made concerning the different strategies for qubit encoding, transport and interaction, including tradeoffs between decoherence rates and the likelihood of twoqubit gate errors. These tradeoffs must be addressed through further refinements of logic protocols and trapping technologies before one can undertake the design of a generalpurpose neutral-atom quantum processor.
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