Heisenberg’s uncertainty principle establishes a “standard quantum limit” of measurement precision that sets a bound on many precision measurements including atomic clocks and gravitational wave detectors. Using a special class of entangled quantum states known as squeezed states, it is possible to exceed the standard quantum limit. I will discuss our experiments investigating spin-1 atomic Bose-Einstein condensates in which non-equilibrium dynamical evolution creates spin-squeezed states with uncertainties an order of magnitude below the standard quantum limit. Additionally, we have developed novel quantum control techniques for the spin states and investigated Kibble-Zurek universality by quenching the spin system across a quantum phase transition. These experiments demonstrate new methods of manipulating out-of-equilibrium quantum systems, drawing together ideas from classical Hamiltonian dynamics and quantum squeezing of collective states.