The article discusses the phenomenon of compounds and idioms as a vital issue in the didactics of translation, exemplified by Polish and German. The author applies Langacker’s cognitive grammar to the description of compound nouns, explains the partial compositionality of complex linguistic units, presents their semantic types and analyses their semantic potential in the press article entitled Grauer Markt (Der Spiegel 2006/32). The cognitive analysis of its translation equivalents comprises the description of the main difficulties related to the translation of particular types of compounds, both literal and non-literal Polish constructions and the explanation of typical errors made by Polish students.