  In this paper, we systematically review mathematical models, theories and
numerical methods for ground states and dynamics of spinor Bose-Einstein
condensates (BECs) based on the coupled Gross-Pitaevskii equations (GPEs). We
start with a pseudo spin-1/2 BEC system with/without an internal atomic
Josephson junction and spin-orbit coupling including (i) existence and
uniqueness as well as non-existence of ground states under different parameter
regimes, (ii) ground state structures under different limiting parameter
regimes, (iii) dynamical properties, and (iv) efficient and accurate numerical
methods for computing ground states and dynamics. Then we extend these results
to spin-1 BEC and spin-2 BEC. Finally, extensions to dipolar spinor systems
and/or general spin-F (F>=3) BEC are discussed.
