This paper revisits some old issues of irony, i.e., situational vs. verbal irony, and irony vs. paradox, in order to further clarify the issues. Although these issues seem to have been fully discussed, there are still unresolved and/or vague aspects that need to be accounted for. This paper also revisits the issue of theorizing the phenomenon of verbal irony, which has long been scrutinized by many philosophers and linguists including Aristotle, Grice, Sperber and Wilson, and recently, Utsumi and Attardo.