Abstract: Recently, experiments on Bose-Einstein condensates (BECs) confined in an optical lattice have made breakthroughs. A research group in Munich has demonstrated for the first time the quantum phase transition of a superfluid state to the Mott insulator state of a BEC confined in a 3D optical lattice. Such a quantum phase transition is not only fundamentally profound, but also provides new access to applications of BECs. This paper reports our recent theoretical work on the spin dynamics and magnetism of BECs confined in an optical lattice, and explores their possible applications in atomic magnetic sensors and quantum computation.