The physics of exceptional points

A short resume is given about the nature of exceptional points (EPs) followed by discussions about their ubiquitous occurrence in a great variety of physical problems. EPs feature in classical as well as in quantum mechanical problems. They are associated with symmetry breaking for ${\cal PT}$-symmetric Hamiltonians, where a great number of experiments have been performed in particular in optics, and to an increasing extent in atomic and molecular physics. EPs are involved in quantum phase transition and quantum chaos, they produce dramatic effects in multichannel scattering, specific time dependence and more. In nuclear physics they are associated with instabilities and continuum problems. Being spectral singularities they also affect approximation schemes.