The interior jelly traces its origin back thousands of years to the candy called Turkish Delight while the shell is essentially the same as developed in the late 19th century for the Jordan almond candy. The two were brought together around the beginning of the 20th century. It was not until 1930 or so that jelly beans became an Easter candy, presumably from their resemblance to eggs.
One prominent maker was the Herman Goelitz Candy Company, also the inventor of candy corn and now renamed the Jelly Belly Candy Company (Fairfield, California) making many naturally flavored beans, including pear, watermelon, root beer, and (their most popular flavor) buttered popcorn. The success of their brand led to a jelly-bean rennaissance, particularly when Ronald Reagan began keeping them on his desk in the White House.
Another product of note which is manufactured by Jelly Belly Candy Company is Bertie Bott's Every Flavor Bean which is named after a product featured in the Harry Potter series of children's books. As in the books, the jelly beans are in many unlikely flavors, including sardine, spinach, earwax, black pepper, horseradish, vomit, dirt, grass, and "booger" as well as more conventional flavors like green apple, chocolate, and watermelon.
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The type was memorialized in the song, "Jelly Bean (He's a Curbstone Cutie)", kept popular through the 1940s by Phil Harris. It was written by Jimmie Dupre, Sam Rosen, and Joe Verges, and published in New Orleans in 1920 by Universal Music Publishers, Inc.