Centering theory is a text-linguistic approach that is not reflected enough in the Czech linguistics. Therefore I firstly introduce the methodological foundations of this theory (background, methodological basis, tools etc.), explain the motivation and classification of the Centers of Attention (forward-looking center, backward-looking center, preferred center) and define different types of Transitions derived from the transformation of Centers of Attention values assigned to the expressions representing the entity in the discourse (continue, retain, smooth- and rough-shift).
Secondly, I highlight some problematic phenomena arising in the preliminary research of the application of the Centering approach on the authentic Czech language material from the Prague Dependency Treebank 3.0 such as the application of the Pronoun rule, Subject rule, the Backward-looking center restriction, issues related to the coreferential expressions within single utterance, complications connected with the covert pronouns. Finally, I try to show how the complications can be solved in practice (subsidiary criteria, parallel annotation of co-referential relations).