On the evening of June 30, 2049, K returned to his apartment where his Joi "prepared" him a virtual dinner, lit his cigarette, and requested him to read a book to her or dance with her. He then gifted her an Emanator, a device that allowed her to become portable. K took her outside in the rain until he was called back to the Los Angeles Police Department headquarters.
Joi later assisted K as he researched the DNA of a child who was born from a replicant. She referenced his memory of hiding a wooden toy horse, which had a date inscribed on it, matching the one K found at the base of a tree on Sapper Morton's farm. She suggested that this could mean that he was actually the child he sought.
K's research found that the replicant had two children, a boy and a girl. The records stated the girl had died of Galatians Syndrome while the boy was processed at the Morrillcole Orphanage in San Diego. K then invited Joi to go to the orphanage with him.
Later at K's apartment, he informed Joi of his conclusion that his memory was indeed real. This overjoyed her, as she always believed him to be special, insisting that he now be called "Joe." Unsure, K sought further information and Joi suggested finding the one responsible for creating memories for replicants.
Joi later hired Mariette to sync with her so that she could have sex with K. Later in the night, after allowing Mariette to leave, K informed Joi that he would soon be hunted by the LAPD, so he must leave. Joi insisted she come with him, convincing him to delete her from his home console, meaning she would only remain on the emanator, increasing the risk of her becoming lost forever.
K took the wooden horse to Doc Badger, who discovered high amounts of radiation, leading K's search to the bombed city of Las Vegas, where Joi accompanied him. There, his search with his drone uncovered heat signatures that indicated life.
There, K found ex-Blade Runner Rick Deckard, the father of the replicant child. Wallace personnel led by Luv attacked the building, taking Deckard hostage and beating K. Joi pleaded with Luv to stop, but was deactivated when Luv stomped on the emanator.
Joi generally appeared as a flawlessly beautiful petite young woman. The specifics of her features, such as eye color, hair color, and wardrobe were variable from instance to instance. She had a variety of vocal intonations and could adopt accents. She was a holographic projection and required some kind of projecting device to manifest to the viewer/user, whether it be a ceiling-mounted projector for a single room, a building-scale advertising projector or a portable "Emanator" device that allowed Joi to travel with her user.
Joi's hardware was able to extensively sense the environment it was in and translated that into data for the artificial intelligence to "experience" life along with the user. The hardware sensed whether Joi was projected or not.
Joi's primary role was to communicate with other entities, human, replicant or otherwise, in a manner representing the user's mate or companion. She recorded data "memories" as she ran, allowing her "personality" to change over time.
Joi's program and memories resided on a main console, which for personal units was located in the home, as well as on portable Emanators or other linked devices. Joi hardware had the ability to utilize communications networks to contact other entities on its own initiative and could be used to monitor or track Joi users.
Was Joi "real?"
Similar to the "Is Deckard a replicant?" question, Joi's existence in the film brings up similar ideas of what is considered real and why it matters.
Joi is real
Several points of view and details in the film indicate Joi to be as real as anyone else in the film. She seems to decide on her own to aid K in evading the police and Wallace Corporation by placing herself in the emanator and breaking the antenna. She claims she wants to be real for K.
From the point of view of K, Joi is for him. She satisfies his emotional needs and more. Is Joi any different than a person shaping themselves to be what one wants them to be?
Joi is not real
Joi is not only just one; she can be purchased by any consumer. You can customize Joi in countless ways and make her who you want her to be. Everything you want to hear and see implies that K's Joi might be following her programming so well that she is simply being what he wants her to be: real. Not because she has grown beyond what she was made for, but because she is doing precisely what she was made for (even calling Joi "she" in this context would be erroneous, where "it" may fit better").
K's encounter with the giant purple Joi ad establishes that Joi has responses that are universal for her product. "What a day" being one of them, she also calls K a "good Joe".
Neither Joi or 'K' are real, but they add up to an agency of free will
'K' is a newer model replicant, which are not human and don't run. Yet 'K' clearly exhibits the agency of free will in the story. Apart from the real memory of a childhood, interaction with Joi may play a part as well. Joi and 'K' are two different artificial intelligent products each consisting different subset of a real person, neither of them are capable of free will on their own, but their connection allowed them to make each other whole.