Irony is often related to humor, both in spoken and written language. One possibility is that humor arises once people reconcile the incongruity between what speakers say and imply when using irony. Humor automatically emerges in these cases given the release of tension following a momentary sense of disparity. Our claim is that this proposal does not capture many of the dynamic complexities in real-world ironic discourse. We describe psychological research on irony understanding showing that ironic meanings are not always understood via a process of drawing conversational implicatures. Studies on people's spontaneous laughter when using irony suggest that the recognition of incongruity between what is said and implied is not necessary for eliciting humor. Laughter occurs at various places in conversation, and not necessarily at the end of speakers' utterances. People also laugh for reasons other than humor, such as to signal affiliation. Overall, finding the humor in irony is not the same as seen in simple jokes, and demands examination of a complex host of contextual factors not always considered in linguistic theories of humor.