The scattering and diffraction of waves through complex media is a paradigmatic phenomenon that has captured the attention of various communities of physics for quite some time now. Recently, there is a lot of interest in composite media that contain spatial distributions of gain and loss materials. Due to the plethora of novel applications, like ultrasensitive sensors and gyroscopes, topological insulator lasers, non-reciprocal ring cavities and single mode nanolasers, such ideas have led to the new area of non-Hermitian photonics.

The first part of the talk will be devoted to localization problems in non-Hermitian disordered media. A generalization of the concept of plane waves and a novel way of propagation that is possible only in non-Hermitian systems will be presented. In the second part of the talk, we will examine the interplay between topological protection and non-Hermiticity around higher order exceptional points and their relation to the underlying theory of pseudospectra. Connection of the above topics to recent experiments will also be examined.