"The Peanut Butter Falcon" is an adventure story set in the world of a modern Mark Twain that begins when Zak (Zack Gottsagen), a young man with Down syndrome runs away from a nursing home where he lives to chase his dream of becoming a professional wrestler and attending the wrestling school of The Salt Water Redneck.

Through circumstances beyond their control Tyler (Shia LaBeouf), a small time outlaw on the run becomes Zak's unlikely coach and ally. Together they wind through deltas, elude capture, drink whisky, find God, catch fish, and convince Eleanor (Dakota Johnson), a kind nursing home employee with a story of her own to join them on their journey.