"The Final Problem" is a short story by Sir Arthur Conan Doyle featuring his detective character Sherlock Holmes. It was first published in The Strand Magazine in the United Kingdom, and McClure's in the United States, under the title "The Adventure of the Final Problem" in December 1893. It appears in book form as part of the collection The Memoirs of Sherlock Holmes.

The story, set in 1891, introduces the criminal mastermind Professor Moriarty. It was intended to be the final Holmes story, ending with the character's death, but Doyle was later persuaded to revive Holmes for additional stories and novels.

An injured Holmes arrives at Watson's residence one evening, having escaped three separate murder attempts that day. Holmes reveals to Watson he has been tracking Moriarty and his organisation for months, who are responsible for most of the crimes orchestrated in London. As Holmes is close to snaring them all and delivering them to the police, Moriarty visits Holmes at 221B Baker Street earlier that day and warns him to withdraw from his pursuit of justice against him. Holmes admits that Moriarty could thwart his plans given his great mind that could rival his, and plans to flee to Europe while the police capture Moriarty and his gang.

Holmes invites Watson to join him on the trip. Holmes then gives him unusual instructions intended to hide his tracks to the boat train at Victoria station before leaving Watson's house by climbing over the back wall in the garden, paranoid that he might be followed. The next day, Watson follows Holmes's instructions and finds himself waiting in the reserved first-class coach for his friend, who is disguised as an elderly Italian priest. As the boat train pulls out of Victoria, Holmes spots Moriarty on the platform trying to stop the train. Holmes deduces that Moriarty has tracked Watson despite extraordinary precautions. Changing their planned route, Holmes and Watson alight at Canterbury, hiding behind the luggage as Moriarty (who had chartered a special one-coach train) passes them in pursuit.

Having made their way to Strasbourg via Brussels, Holmes receives a message from the London Police that most of Moriarty's gang have been arrested in England, but Moriarty has escaped and is in pursuit of Holmes in Europe. He urges Watson to return to England as he considers himself a very dangerous companion for Watson. Watson, however, decides to stay with his friend. Holmes and Watson continue to Meiringen, Switzerland and visit the Reichenbach Falls. At the Falls, a boy hands Watson a letter, saying that there is a dying Englishwoman at the hotel who seeks an English doctor. While Holmes realises it is a hoax, he allows Watson to go.

Watson soon realises the trick when returning to the hotel and rushes back to the Falls. He only finds two sets of footprints that lead to the end of the path, where he uncovers other signs of a violent struggle and a note from Holmes explaining that he knew about the hoax but chose to fight Moriarty himself. Holmes and Moriarty have apparently both fallen to their deaths down the gorge and their bodies cannot be recovered. A saddened Dr Watson returns to England. The Moriarty gang are all convicted on the strength of evidence secured by Holmes. Watson ends his narrative by saying that Sherlock Holmes was the best and the wisest man he had ever known.

"The Final Problem" was intended to be exactly what its name says. Doyle meant to stop writing about his famous detective after this short story; he felt the Sherlock Holmes stories were distracting him from more serious literary efforts and that "killing" Holmes off was the only way of getting his career back on track. "I must save my mind for better things," he wrote to his mother, "even if it means I must bury my pocketbook with him."

Doyle sought to sweeten the pill by letting Holmes go in a blaze of glory, having him rid the world of a criminal so powerful and dangerous that any further task would be trivial in comparison; indeed, Holmes says as much in the story.