In this talk, the inverse problems of determining unknown/inaccessible obstacles by acoustic or electromagnetic scattering far-field measurements shall be addressed. We shall review the uniqueness and identiability results obtained by using scattering amplitude or a single far-field measurement. Then we talk about the qualitative numerical reconstructions. In the last part of the talk, we shall present our recent study on making the obstacles virtually reshaped or invisible to detections by metamaterials cloaking.