Main basic methods of analysis and assimilation for numerical weather prediction (NWP) has gone through the polynomial function fitting method, the successive correction method (SCM), the optimum interpolation (OI), the variational method (Var) and the ensemble Kalman filter (EnKF). This article tries to present a concise and true description with their basic ideas and implementation approaches based on original classical references to these methods. Then remarks on their distinct characteristics and innovative development are made, and it is highlighted, from these remarks, that we can see a stepbystep expansion of useful information and cutdown on limitations along the historical progress of atmospheric data assimilation, which is clearly endowed with a foreandaft connection and a cognitively simple internal logic of development. Also, an effort is taken to precisely understand the concept of “atmospheric data assimilation”, along its historical progress and on basis of some essential terms “subjective analysis” and “objective analysis”, “first guess field” and “background field”, “analysis” and “assimilation”, “update”, and “innovation”.