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This is a survey on selected developments in the theory of natural dualitieswhere the author had the opportunity to make with his foreign colleaguesseveral breakthroughs and move the theory forward. It is aimed as author'sreflection on his works on the natural dualities in Oxford and Melbourne overthe period of twenty years 1993-2012 (before his attention with the colleaguesin universal algebra and lattice theory has been fully focused on the theory ofcanonical extensions and the theory of bilattices). It is also meant as aremainder that the main problems of the theory of natural dualities,Dualisability Problem and Decidability Problem for Dualisability, remain stillopen.  Theory of natural dualities is a general theory for quasi-varieties ofalgebras that generalizes `classical' dualities such as Stone duality forBoolean algebras, Pontryagin duality for abelian groups, Priestley duality fordistributive lattices, and Hofmann-Mislove-Stralka duality for semilattices. Wepresent a brief background of the theory and then illustrate its applicationson our study of Entailment Problem, Problem of Endodualisability versusEndoprimality and then a famous Full versus Strong Problem with relateddevelopments.

On selected developments in the theory of natural dualities