  Scattering of electromagnetic waves lies at the heart of most experimental
techniques over nearly the entire electromagnetic spectrum, ranging from radio
waves to optics and X-rays. Hence, deep insight into the basics of scattering
theory and understanding the peculiar features of electromagnetic scattering is
necessary for the correct interpretation of experimental data and an
understanding of the underlying physics. Recently, a broad spectrum of
exceptional scattering phenomena attainable in suitably engineered structures
has been predicted and demonstrated. Examples include bound states in the
continuum, exceptional points in PT-symmetrical non-Hermitian systems, coherent
perfect absorption, virtual perfect absorption, nontrivial lasing,
non-radiating sources, and others. In this paper, we establish a unified
description of such exotic scattering phenomena and show that the origin of all
these effects can be traced back to the properties of poles and zeros of the
underlying scattering matrix. We provide insights on how managing these special
points in the complex frequency plane provides a powerful approach to tailor
unusual scattering regimes.
