Psychology Today posted a summary of a study showing the aerobically fit kids are, essentially, smarter than unfit kids.
"Smarter" (my word, not the researchers' or article author's) here means children who were more physically fit had "faster and more robust neuro-electrical brain responses while reading" and "had better language skills" The article goes on to summarize: "These language skills were linked to brain synapses that fired with more strength and faster speed."
According to the article citing the study from the University of Illinois at Urbana-Champaign, there's a "direct correlation between fitness levels and cognitive performance on a variety of tasks."
None of this comes as any real surprise to me, although I'm glad we have science proving these points. However, I'd be curious to see this study done including young adults and teens who are of normal intelligence but have other physical limitations, such as being confined to a wheel chair or have severe asthma, that make it difficult to get aerobic exercise.