Israeli Psychologists Studies: Participants with pre-frontal lobe damage had the most difficulty comprehending sarcasm.

L. hemisphere interprets the literal meaning of the utterance.

R. hemisphere and frontal lobes process the intentional, social, and emotional context, identifying the contradiction between the literal meaning and context.

The right ventromedial prefrontal cortex integrates the literal meaning with the social/emotional knowledge of the situation and previous situations, helping the listener determine the true meaning. (American Psychological Association. The Anatomy of Sarcasm: Researchers Reveal how the Brain handles this Complex Communication, 2005. Article.)