From an interesting Economist article headlined "Who owns Sherlock Holmes?":
No one disputes that the copyright has expired on Conan Doyle's work anywhere where protection ceases 70 years after an author's death (he died in 1930). Yet when America reformed its copyright rules in 1978 to introduce a "life plus" model in harmony with the rest of the world for works created starting in 1978, it retained its older term-limited system for property created between 1923 and 1977. Works produced within that range have had their expiration extended to a fixed 95-year term from first publication; anything produced earlier is in the public domain. This umbrella of protection covers ten Holmes stories published in America for the first time as part of "The Case-Book of Sherlock Holmes" in 1927. These stories are still under copyright until January 1st 2023.
Not surprisingly, that means you need the Doyle estate's permission to reprint or adapt one of those 10 tales. Perhaps more surprisingly, it means you need its permission to publish an original Sherlock Holmes story that mentions some in-universe fact that first appeared in one of those tales. Sherlock Holmes himself is in the public domain, but when it comes to certain elements of the Holmes mythos, the law gets trickier.
Posts like this tend to set off debates in the comments about whether copyright laws should exist at all, but let's assume, for the sake of argument, that they should. Can anyone give me a good reason for applying copyright to a character, as opposed to a story about that character? It shouldn't be difficult for the fans of, say, Star Wars to tell which stories about Han Solo have George Lucas' input or blessing and which ones do not. Why shouldn't you have the legal right to circulate your own Han Solo films or novels on more than a semi-clandestine amateur basis without asking permission first, competing head to head with Disney to see who can tell the better stories about the characters and settings that Lucas invented? I can see why Disney's shareholders wouldn't like that, but why should their preferences be law?
And suppose we agree that characters should be copyrightable. Why on Earth should intellectual property law protect particular characteristics of a public-domain character? Does it really make sense to have a legal regime in which anyone can write a story about Sherlock Holmes but you need to pay tribute to Arthur Conan Doyle's heirs if you allude to the wrong elements of the canon?
The Doyle estate, meanwhile, seems to think it has legal control over even more than those 10 short stories. Read the Economist feature for the details.