The crystals associated with integrable modules of quantum affine algebras can be realized as subsets of semi-infinite tensor products of certain finite crystals called perfect crystals. In particular for the quantum affine algebra of special linear type these crystals have a nicer presentation in terms of colored Young diagrams. The crystals for Demazure modules are finite subsets of the crystals for the associated integrable modules. In this talk we will present some old and new results on the Demazure crystals.