Department of Mathematics (Faculty of Philosophy, University of Niš), in 1991 celebrated 20 years of its foundation. On that occasion, Department of Mathematics organized a conference ``Filomat 20'' from $26^{\operatorname{th}}-28^{\operatorname{th}}$ September 1991. I would like to give a paraphrase and extension of my talk. Of course, it is not a complete review of the essential spectra of single operator (see for example [76]), it is just a glimpse. Let me apologize for the lack of complete credits and references.