The article discusses the concept of realia within the framework of cognitive semantics and cognitive-heuristic approach to translation. The study is conducted on the basis of plays by A.N.Ostrovsky and their English translations made by native speakers of English. First, the paper explores the traditional approach to realia and the suggested strategies of their translation, and identifies problems stemming from the traditional approach. The latter include, among other things, the lack of strict criteria for identifying realia, ignoring the factor of the cognitive context and excessive use of pragmatic additions. At the second stage, we identify culture-specific units in the texts of the plays and, using the method of introspection, model first the process of cognitive search and then, on the basis of the English translations, the process of encoding the meanings of the ST units in the TT. The study has revealed a number of interesting regularities. Many of the culture-specific units lose their specificity in context, some others come to acquire new meanings. The translators apparently take into consideration the notions, knowledge and expectations of the TL audience, and the factor of naturalness. The study shows that first, far from being untranslatable, the various culture-specific units found in the ST are not especially hard to translate compared with other, non-culture-specific units. Second, in the way they are translated, they do not differ much from many other units, but can differ from each other. The conclusion is made that there is not sufficient reason to assign the units in question to one single identifiable group in terms of their translation, and that the use of the term “realia” in translation studies is just a matter of convention.