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The Undoing on HBO is based around the central mystery of who killed Elena Alves (played by Matilda De Angelis), but has not given us much in the actual way of clues. Though Jonathan Fraser (Hugh Grant) is currently charged with the murder, he professes his innocence, and at the end of Episode 4 during an interview, he says he will reveal who really killed Elena. Here's who viewers of the show think might have committed the crime.
All the main theories about who killed Elena in The Undoing
WARNING: The following reveals the ending of the book The Undoing is based on, "You Should Have Known."
Jonathan

Maybe the answer is hiding in plain sight, and the person who the police think did it actually is the murderer. After all, he had been having an affair with Elena, even fathering a child with her, and clearly has been keeping a lot of secrets from his wife Grace (Nicole Kidman).
In the book, Jonathan is the killer, murdering Malaga (the name the Elena character has in the novel) as she gets pregnant with his child again). However, the show has already deviated significantly from the book—for example, Jonathan never returns in You Should Have Known after first disappearing. This likely suggests that we're heading for a very different ending in The Undoing.
Grace

While the show is seemingly about all the things Grace does not know about Jonathan, could it be Grace that we really know nothing about, who is pretending to know nothing about her husband's affair but really knew everything and took matters into her own hands?
She says that she has no memory of being close to Elena's apartment on the day of the murder, but CCTV proves she was there, so either she is lying or she is having dissociative episodes—either of which could point to her being the killer.
Fernando

In killings such as this, the husband is always the prime suspect, so we should not rule out Elena's spouse Fernando (Ismael Cruz Cordova) killing her after finding out that his wife has been cheating on him and his son is not his.
In a show as twisty and turny as The Undoing, the husband might be too obvious a solution, but it's certainly possible that he knows more than he's let on.
Franklin

Grace's father Franklin (Donald Sutherland) has proven time and time again that he is willing to use his many resources to make a problem go away, like when he loaned money to Jonathan to get Elena's kid into Reardon to stop Elena revealing all.
There are two possible ways therefore that Franklin could have been involved: Either he decided to deal with the Elena problem once and for all, or he decided to frame Jonathan after becoming tired of the many ways in which he has lied to his daughter over the years.
Henry

A more farfetched theory but still possible in a twist-filled drama like The Undoing: Grace's son Henry (Noah Jupe) killed Elena after finding out about the affair and panicking that this would break up his parents. Not only would this be a huge twist, but it would fit the themes of The Undoing—maybe Grace knows nothing about the secrets of both men in her direct family.
The school moms
The Undoing sees Nicole Kidman team up again with Big Little Lies creator David E. Kelley. But have they also brought with them the ending of the first season of that show, where (major spoilers ahead) the school moms kill Nicole Kidman's character's bad news husband together? Probably not, though it is possible.
The Undoing airs Sundays at at 9 p.m. on HBO.