One of the earliest proposals for scalable quantum computers was optically trapped, ultracold neutral atoms. Like their more famous cousins, atomic ions, qubits encoded in the energy levels of neutral atoms are all identical, can have long coherence times, and can be controlled with a variety of magneto-optical fields, with tools that build on decades of development for atomic clocks and precision metrology. Unlike with ions, quantum computing architectures have proceeded more slowly, as neutral atoms are harder to trap and they only weakly interact in their ground state. New developments in trapping and laser technology has now opened the door to high-fidelity operation with potentially hundreds to thousands of qubits - neutral atoms are back in the game! In this seminar I will discuss how high-fidelity quantum logic can be implemented through coherent control of superpositions of atoms in ground and highly excited Rydberg states. I will also describe how optimal control can be used to implement a variety of protocols for quantum information processing with neutral atoms, including the performing quantum logic with “qudecimals" (d=10 dimensional systems) encoded in nuclear spins.