An iterative process of continuation of wave fields is proposed to invert the wave equation. Inverse problems of two types are analyzed, namely: the problem of reconstruction of the right-hand side of the wave equation describing the wave sources and the inverse problem of wave scattering in an inhomogeneous medium. The latter problem is of great practical importance for applications. It is shown that for an observation system in which a source point coincides with a receiver point (the so-called "scheme of central rays" in seismic prospecting), the scattering problem is reduced to the Cauchy problem on a space-like surface and in an inhomogeneous reference medium. The solution of this problem is obtained by wave continuation at each iteration step with the reference velocity values specified at the previous step.