A short resume about the nature of EPs followed by a discussion about their ubiquitous occurrence in a great variety of physical problems. EPs feature in quantum phase transition, quantum chaos, they produce dramatic effects in multichannel scattering, specific time dependence and more. In nuclear physics and in fermion gases they are associated with instabilities and affect approximation schemes. EPs could be of interest for weakly bound states such as halos realized for nuclei along the drip line and at formation of molecules for colliding atoms at low temperatures.