Using background error covariance to construct dynamic balance constraints is very important to the design of variational assimilation schemes. It can permit a multivariate analysis, increase the value of each individual observation, and also improve the preconditioning of variational assimilation schemes. In this paper, the basic method and process of incorporating dynamic balance constraints are first surveyed.Based on this, the common problems of constructing the widelyused quasigeostrophic and hydrostatic balance constraints in global and limited domain assimilation schemes are reviewed.Three constructing quasigeostrophic balance constraint methods are discussed, including dynamic balance equation method, statistical method, and dynamicstatistical combined method.The undetermined problems of constructing hydrostatic balance constraint in different vertical grids and their solutions are also surveyed.Finally, the future challenges and opportunities of constructing dynamic balance constraints using background error covariance in special areas (such as tropics), in designing high resolution assimilation schemes and ensemblevariation hybrid schemes are discussed.