This recent study sorted out the difference between recognizing that something's funny and emotionally responding to it. It turns out the 'getting' the joke is processed more on the analytical L brain, whereas emotionally responding to it is on the right.
Humor is a 'secret weapon' of great teachers and leaders because it diffuses anxiety and, when used expertly, can focus attention. I have to say that I still vividly recall some lectures from my college days at Harvard (over 20 years ago!) because professors had many joke slides and pulled stunts (like my Organic Chem professor dressing up as a Canadian Mountie). Some links to humor and teaching are posted below.
Problems with humor are often noted in children suspected of having high functioning autism or Aspergers syndrome - but you might expect, the reasons for not getting jokes are diverse as differences in brain function. Problems that occur on the L side of the brain, the R side of the brain, or both, can affect your recognition or appreciation of humor.
Auditory processing delays will affect timing (every comedian knows how important timing is), visual processing problems can interfere with 'reading' visual body or facial expressions, and problems with empathy, emotion responsiveness, or theory of mind will cause other problems. Because humor is so important for social communication and interpersonal relationships, it is worth teaching children if there are problems. Some social skills programs for children with autism spectrum disorders (like Michelle Winner's below) strongly incorporate humor and its teaching.
Using Humor in the Classroom
Humor and Multiple Intelligences
Humor In College Teaching In "Dread Courses"
Humor in High Functioning Autism and Aspergers Abstract
Humor n in Autism and Aspergers Abstract
Michelle Winner - Social Thinking