Data assimilation systems combine a short-range forecast with the latest observational information. The effective representation of forecast and observation errors is an essential aspect of such systems. Each forecast contains O(10^7) variables: error correlations are approximately homogeneous and isotropic but there is an interplay of horizontal and vertical scales with some latitude dependence. Current methods for representing these stationary error patterns will be summarised. In addition there is growing interest in how to model departures from stationarity (such as larger errors associated with particular weather features) and departures from normal distributions (for moisture variables in particular).