I will start with the definition of the metastable states as dynamical (temporal) states of the system, relaxing to equilibrium, before the equilibrium is reached. I will explain then that in general one should not expect these states to be Gibbs states.

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.