abstract: The talk describes the posibilities and limitations of the Kaczmarz method for the inverse problem of the wave equation in time domain. In particular we study the role of the source wavelet, of reflectors, of finite apertures, and of evanescent waves. We suggest highly efficient implementaions based on finite difference methods. We also discuss convergence in dependance of the initial approximation. We present numerical example from ultrasound tomography and seismic imaging