It was noticed in the early 1960s that a large amount of RNAs is associated with chromatin. What kind of RNAs are they? Where are they located on chromatin? When and in what processes do these RNAs perform their physiologically normal or pathogenic functions? The review describes the modern approaches that help, to some extent, to answer these questions. Consideration is given to the experimental methods that make it possible to obtain the complete RNA-chromatin interactome of a cell or the genome-wide interaction maps of individual RNAs with chromatin, as well as the methods to process the experimental data. Focus is placed on the noncoding RNAs that function in close contact with chromatin and chromatin-associated protein complexes. A variety of biological examples described using the methods makes it clear that RNAs interacting with chromatin play an important role in the functions of cell systems by finely tuning the chromatin architecture and thus changing the level of gene expression.