Scattering of acoustic or electromagnetic waves plays an important role in many areas of the applied sciences - medical imaging, ultrasound tomography, material science, radar, remote sensing, aeronautics, and seismic exploration. This book provides a survey of recent developments in inverse acoustic and electromagnetic scattering theory. Special emphasis is placed on the methods developed during last five years, which use point-sources combined with several far-reaching techniques to obtain qualitative reconstruction methods. The book addresses questions of uniqueness, stability, and reconstructions for both two- and three-dimensional problems.