In philosophy, problems arise from consideration of precisely what is supposed to correspond with what. Statements themselves are mere physical things (for example, ink on a page) with no intrinsic meaning. So it is usually claimed that it is the proposition (or meaning) expressed by a statement that corresponds with the facts. Yet both these "entities", propositions and facts, may be unappealing to minimalists who refuse to admit such abstract entities to their ontology.
Another question is exactly what "correspondence" means.
See also the article on truth, which deals with some of the philosophically-heavy issues surrounding the correspondence theory.