Abstract: Bose-Einstein condensates (BECs) are ultra-cold gases, in which all atoms have a single collective wavefunction for their spatial degrees of freedom. With an additional spin degree of freedom, spinor BECs constitute a collective quantum system offering an unprecedented degree of control over such parameters as spin, density, temperature, and the dimensionality of the system. Spinor BECs have thus been considered as good quantum simulators for verifying and optimizing condensed matter models. In this talk, I will discuss a novel quantum phase transition realized in our antiferromagnetic spinor BEC system. I will also present our experimental study on nonequilibrium dynamics of a spinor BEC after it is quenched across a superfluid to Mott insulator phase transition in cubic lattices. Intricate few-body dynamics consisting of spin-mixing oscillations at multiple frequencies are observed after distinct quantum quench sequences. We confirm these observed spin-mixing spectra can be utilized to reveal atom number distributions of an inhomogeneous system, to study transitions from two-body to many-body spin dynamics, and to precisely measure two key parameters determining the spinor physics.