America, 1926: a young British magizoologist by the name of Newt Scamander arrives in the city of New York on his way to Arizona. As he makes his way through Manhattan, he pauses to listen to the ramblings of Mary Lou Barebone, the leader of a group known as the "Second Salemers" who claim that witches are real, living among them and posing a grave danger. While listening to her, something escapes from Scamander's suitcase: a Niffler, a mischievous creature with a perchant for swiping anything shiny. Worse still, Barebone is ranting on the front steps of a bank, where the Niffler swipes at gold and coins.
While Scamander manages to catch it, he ends up being witnessed by a No-Maj (the American term for Muggles) named Jacob Kowalski, a cannery worker who came to the bank in the hopes of taking out a loan to open his own bakery. When Scamander tries to wipe his memories of his chasing the Niffler and using magic, Kowalski escapes. Shortly afterward, Scamander is apprehended by Tina Goldstein, an employee of the Magical Congress of the United States of America, who take the secrecy of the magical world very seriously, to the extent where contact between wizards and No-Majes is heavily regulated, if not outright prohibited. With Scamander in her custody, Goldstein, who had been demoted from her post as an Auror, tries to have Scamander arrested for his having let a magical creature loose and allowing a No-Maj to witness it.
Unfortunately, the only proof, the suitcase that Scamander keeps magical creatures in, wound up getting swapped with a No-Maj's briefcase filled with various pastries. As Scamander is released, Jacob, downtrodden by his inability to get a loan for lack of collateral, had accidentally taken Scamander's suitcase and accidentally releases some of the creatures contained therein, getting bit by one such creature as the others run amok in Manhattan.
Scamander and Goldstein make their way to Jacob's apartment, which had been destroyed by some of the magical creatures that escaped. Scamander manages to capture the one that had attacked Jacob. After repairing the apartment, Tina takes Scamander and Jacob to her apartment, so they can observe the No-Maj to monitor his health. There, Scamander and Jacob meet Queenie, Tina's sister, whom Jacob takes a shine to.
That night, while pretending to sleep, Scamander invites Jacob into his briefcase while he tended to the creatures contained therein, introducing Jacob to a world of magic the likes of which he could never imagine. Therein, Jacob discovers Scamander's reason for coming to America: he had rescued a Thunderbird from an illegal trading ring in Egypt and came to release it back in its habitat in Arizona. In the meantime, he enlists Jacob's aid in re-capturing the creatures that had escaped. Together, they manage to recapture a female Erumpent in heat.
While Scamander and Jacob are inside the briefcase after capturing the Erumpent, Tina captures the briefcase and brings it to the MACUSA office. With Scamander and Jacob now in the custody of the MACUSA, they learn that the wizarding world is in a crisis: one creature has killed a No-Maj senator, placing the secrecy of wizards in jeopardy. Scamander, upon seeing the body, recognizes the damage done to it as the work of an Obscurus, a destructive parasitic mass of magical energy that is created from children who repress their magical abilities, often killing the child in the process. Scamander had extracted an Obscurus from a child who had died and kept it in his suitcase in a protective barrier. When Percival Graves, a high-ranking Auror in the MACUSA, discovers Newt's Obscurus, he accuses him of conspiring with Gellert Grindelwald, an extremely dangerous wizard criminal who aimed to reveal the existence of wizards and conquer the world of No-Majes. As such, Graves orders Scamander and Goldstein to be executed immediately.
Thankfully, the two manage to escape while Queenie saves Jacob from having his memories wiped. Together, they manage to re-capture the last two creatures that escaped Scamander's briefcase: an Occamy and a Demiguise.
Unbeknownst to them, and the MACUSA, Graves was conspiring with a young man named Credence, one of the children adopted by Barebones and the one most often abused by his mother, to find the Obscurus that was loose in the city for his own ends. He initially believes the Obscurus to be one of Credence's siblings. He soon discovers that the true Obscurus was Credence, himself: originally thought to be a Squib (one born to magical parents but lacking the ability to use magic, themselves), he had survived to adolescence in spite of having repressed his magical powers well past the point where doing so would kill any other child, and his Obscurus was thus extremely destructive.
Credence reaches his limit and unleashes his Obscurus, carving a swath of destruction through Manhattan and drawing attention from the No-Majes to the existence of magic! Credence, now in the form of a mass of uncontrollable magical energy, hides in a subway tunnel. Scamander goes after him and tries to talk him down. He is joined by Tina, who had known Credence previously and had attacked her mother when she witnessed her abusing him (costing her commission as an Auror in the process). Before they can talk him down, however, the American Aurors arrive and, having determined Credence to be too dangerous, destroy him.
Graves becomes upset at the Aurors destroying Credence, having meant to use him to expose the existence of wizards to the No-Majes, claiming that the MACUSA's laws concerning their secrecy was for the benefit of No-Majes. He attacks the Aurors, but Scamander manages to subdue him. He uses a spell on Graves to remove his disguise, revealing his true identity to be none other than Gellert Grindelwald himself!
As Grindelwald is taken into custody, concerns linger of the wizarding world being exposed to No-Majes. Scamander, however, has a solution: he releases his Thunderbird in Manhattan with a special potion that mixes with a rainstorm that the Thunderbird creates, erasing all of the New York No-Majes' memories of the events that transpired while Aurors repaired the damage inflicted upon the city. Unfortunately, Jacob must have his memories erased as well, as per MACUSA law. Scamander, Tina, and Queenie say their farewells to Jacob before he steps into the rain, Queenie, who had mutual feelings for Jacob, kissing him before the three wizards leave.
Having completed what he set out to do, Scamander says his farewells to Tina (who had been reinstated as Auror), but promises to return to hand-deliver her a book based on the manuscripts he wrote about the creatures under his care, titled Fantastic Beasts and Where to Find Them. Before he departs for Europe, however, he leaves Jacob with a briefcase filled with highly valuable Occamy egg shells. With those shells, Jacob is finally able to secure funding for his bakery, where he reunites with Queenie.