The problem of state estimation has come to be known as "data assimilation" in many geophysical applications. I will review data assimilation for the atmosphere, especially for numerical weather prediction. A distinguishing characteristic of atmospheric data assimilation is the diversity and extremely large numbers of observations considered and the extremely large dimension of the state vector. Monte-Carlo techniques have had a major influence on atmospheric data assimilation in the last 15 years and numerical weather prediction has been a crucial high-dimensional testbed for Monte-Carlo approaches. I will discuss two interesting aspects: i) the use of the a priori assumption that state correlations are spatially local, when estimating the covariance matrices needed in linear, least-squares assimilation schemes (such as the ensemble Kalman filter), and ii) the potential for particle filters in high-dimensional systems.