We give a characterization of the crystal bases of Demazure submodules
of a level-zero extremal weight module over a quantum affine algebra.
This characterization is given in terms of the initial directions of
semi-infinite Lakshmibai-Seshadri paths (SiLS paths), and is established
under a suitably normalized isomorphism between the crystal basis of
the level-zero extremal weight module and the crystal of SiLS paths.
This talk is based on a joint work with Satoshi Naito (arXiv:1404.2436).