In this paper

the author firstly provides a brief review of the progress of theory wave-field inversion from two aspects

namely

theory and method of the nonlinear inversion problem.On the bases of a brief historical retrospect of the nonlinear inversion problem.On the basis of a brief historical retrospect of the nonlinear inversion method in recent years

the author concludes the newest advances in the familiar nonlinear inversion method research

makes some comparisons and comments on some problems consisting in the nonlinear inversion method

at the same time points out some problems existing in the nonlinear inversion method at present

and at the end gives some expectations for new advancing direction of the nonlinear inversion theory.