Self-referential statements are sentences that refer to themselves in some way. For example, the statement "This sentence is five words long" describes its own length. These statements can create interesting puzzles and paradoxes, as they often challenge our understanding of language and meaning. In logic and philosophy, self-referential statements can lead to complex discussions, such as the famous liar paradox, which involves a statement that declares itself to be false. Such statements highlight the intricacies of language and the potential for contradictions, making them a fascinating area of study in both linguistics and mathematics.