The Deathly Hallows marks the culmination of the Harry Potter franchise, with it featuring the defeat of Voldemort in an epic battle. The story was so grand, in fact, that the novel was divided into two films that saw Harry, Ron and Hermione find out about the Deathly Hallows and their pivotal part to play in the fight against the dark forces. However, after the Battle of Hogwarts and Voldemort's death, the fate of the objects is a bit up in the air.
In the Wizarding World, the Deathly Hallows pertain to an old story, The Tale of the Three Brothers. After using magic to build a bridge over a river, a personification of Death appears to the three Peverell brothers to congratulate them on escaping him and offer each a magical gift -- to Antioch Peverell, the Elder Wand, to Cadmus Peverell, the Resurrection Stone, and to Ignotus Peverell, the Cloak of Invisibility. However, these objects are a trick that Death uses in order to claim the brothers’ lives, with the exception of Ignostus, who cleverly uses the cloak to evade Death until he's ready to move on.
After becoming part of Harry's journey, the Deathly Hallows quickly become MacGuffins, just like the Horcruxes and the Sword of Gryffindor. Of course, Harry was already in possession of the Cloak of Invisibility since his first year at Hogwarts, which left only two to locate. Unfortunately, Harry had a vision that Voldemort was seeking the Elder Wand, which the evil wizard eventually found in Dumbledore’s grave. However, after realizing the Resurrection Stone was hidden inside the Golden Snitch left to him by Dumbledore and that he was the true master of the Elder Wand all along, Harry defeats Voldemort and takes possession of the wand.
But just like in The Tale of the Three Brothers, only one of the Deathly Hallows has a meaningful future. In Deathly Hallows: Part II, after the Battle of Hogwarts, the Elder Wand is given a different fate from the book, while the location of the other two objects is left more to speculation. In the film, after defeating Voldemort, Harry snaps the Elder Wand in two and throws it away, while, in the novel, Harry returns the wand to Dumbledore’s grave, assuming that, if and when he dies a natural death, its power will be broken.
As for the Resurrection Stone, Harry uses it in the Forbidden Forest before meeting Voldemort in order to contact his dead parents, as well as Sirius and Lupin. But after deciding to accept his fate and die at Voldemort's hand, he drops it on the ground in the forest and steps away as the figures of his loved ones vanish. As the Peverell brothers' story cautioned, too much contact with the dead could drive the living insane, so it was probably for the best that Harry left it and decided to move on.
Finally, it's been more or less confirmed that the Cloak of Invisibility remained in Harry’s possession. The cloak was given to Harry by Dumbledore during his first year at Hogwarts because it belonged to his father, James, which can be seen as a parallel to how Ignotus gave it to his own son before passing on. And, as fate would have it, Harry would pass the cloak to his own son, James, continuing the tradition of the object being the most important Deathly Hallow in the Wizarding World.