In this talk, I will review our results on mathematical analysis and numerical simulation for Bose-Einstein condensation (BEC). As preparatory steps, we take the three-dimesnional (3D) Gross-Pitaevskii equation (GPE), scale it to obtain a three-parameter model and use an approach well known in the physical literature to reduce it to 2D and 1D GPEs in certain limiting regimes. Mathematical analysis results on ground state and dynamics of BEC are presented. Efficient and accurate numerical methods for computing grund state and dynamics of BEC are reviewed. In addition, comparison with experimental results on collapse and explosion in 3D is reported. Finaly, stability and interaction of quantized vortices in BEC are discussed.