Data assimilation for numerical weather prediction deals with numerical models that have very high dimensions. The scalability of algorithms is limited by several factors, including the required memory, computational load, communication over bus traffic, and the degree of parallelism. The sizes of covariance and Jacobian matrices are beyond the limits of computer memory and bus traffic. In this presentation, we will first review some existing algorithms of data assimilation, including 4D-Var and EnKF. Then some new ideas on nonlinear filtering for data assimilation will be introduced and illustrated using examples.