Full summary that I found:

Movie opens with Madeleine as a child. Her mother gets killed by Safin, who chases Madeleine until she breaks into a frozen sea. There, he saves her life. Then we see Bond and Madeleine right after Spectre hanging out in Matera, talking about Vesper. Bond goes to Vespers grave, after Madeleine insists. The tombstone explodes, Bond is chased by, goes back to the Hotel, grabs Madeleine, huge action scene. He leaves her, thinking she betrayed him. Title sequence.

5 years after the Matera scene, a scientist is kidnapped from a secret MI6 lab. He has developed nanobots that spread like a virus as soon as one infected person touches another. The nanobots can be coded to specific DNA strands, so are only dangerous if they are programmed to your genetic code. Bond is hanging out in Jamaica and is sought out by Felix Leiter and another CIA guy. They want his help, he refuses. That same night Nomi shows up, the new 007, through whom he gets some new info. He calls M, and reproaches him heavily, since the Nanobot project was commissioned by M himself for years.

Bond calls Felix and accepts after all. He flies to Cuba and meets with Paloma. Together they infiltrate a Spectre meeting with the aim of tracking down the kidnapped scientist. They walk into a trap. Blofeld can be heard over loudspeakers and wants to kill Bond by releasing the "bioweapon." But when it is deployed, all the Spectre members die instead of Bond. The scientist had reprogrammed the nanobots on Safin's behalf so that they would not kill Bond but destroy Spectre.

Bond and Paloma grab the scientist, Nomi shows up briefly but is cut down by Bond. There is a long action scene. Paloma disappears from the film relatively suddenly. Bond and the scientist fly two by two onto a boat, where they meet up with Felix and his CIA colleague. The colleague turns out to be a traitor, shoots Leiter, escapes with the scientist, and blows up part of the ship. Bond tries to save Leiter, but it's no use. Felix dies in the sinking ship, Bond barely escapes.

He goes to MI6, but M is stubborn and sends him away. With Moneypenny and Q's help, they discover enough clues to be granted a conversation with the imprisoned Blofeld. Problem is, Blofeld has been talking to only one person for years. Madeleine.

Safin visits Madeleine in London and blackmails her into infecting herself with the virus and killing Blofeld with a simple touch. She plans to make it happen. Together with Bond they visit Blofeld in the cell, in the process Bond touches Madeleine on the hand and unknowingly infects himself. Madeleine does not go through with the action and leaves early. Blofeld confesses to Bond that he deliberately staged it 5 years ago as if Mafeleine was a traitor. It was his revenge on Bond. Bond freaks out, grabs Brother Ernst by the collar and in the process transfers the "virus" aka the nanobots to him. Blofeld dies. Q and co realize that Bond must have been infected by Madeleine.

Bond goes to Norway to the house from Madeleine's childhood and confesses his love to her. There he learns that Madeleine has a little daughter, about four years old. She claims that it is not his. Madeleine then confesses to him who Safin is: when he was a boy, his parents were murdered by Mr. White. This prompted him to once seek revenge on the family by killing Madeleine's mother - and now to take out Spectre, who ordered his family's murder. Through Nomi, Bond learns that Safin is on his way to meet them, so they escape in a jeep. What follows is a long car chase through the countryside. At some point, all 3 get out and Bond separates from Madeleine and her daughter to kill the attackers on him. He takes out almost everyone, and among others kills the CIA traitor in revenge for Leiter, but Safin is able to capture Madeleine and her little daughter.

Thanks to Q, Bond and Nomi (who gives Bond the number 007 back) find out that Safin lives on an island between Japan and Russia, where there is an old World War II base. Using the CGI plane from the trailers, they infiltrate Safin's headquarters and learn that he plans to use the nanobots to murder millions of people on the planet. They realize they must destroy the base. First, however, Nomi takes the scientist hostage, while Bond meets Safin, who has Madeleine's young daughter with him. In the dialogue that follows, it becomes clear that the girl is very much Bond's daughter. Bond tricks Safin, kills his men, but Safin escapes. However, the daughter is able to escape Safin independently later and shortly after that, Nomi, Bond, Madeleine and the girl are united. Nomi kills the scientist in between when she no longer needs him as a hostage.

Nomi, Madeleine and the daughter leave the base, Bond stays behind alone. Since M has ordered a missile strike on Safin's island, Bond must open large missile silos there so that the missiles really destroy the headquarters (and thus the possibility for Safin to produce more of the nanobots) and not bounce off the outer facade. In the process, he fights his way across a bunch of men; there's a long one-take scene in a stairwell that's very reminiscent of "Atomic Blonde." Finally, he is shot several times by Safin, but is able to overpower him. Safin tells him that he has infected Bond with new nanobots programmed with the genetic code of Madeleine and her daughter. So he would kill them both if he ever touched them again. He then shoots Safin with several bullets.

Bond opens the silos and asks Q to connect him with Madeleine. He tells her that he loves her and that she now has all the time in the world with her daughter. She tells him that the girl has his eyes. He says, "I know." Then the missiles arrive on the island and Bond is engulfed in a fireball. He is definitely dead. It's not left open, he's as dead as dead can be. In M's office, all the MI6 staff raise their glasses to Bond, while Madeleine and her daughter take the car to Matera, where she says to the little girl, "I want to tell you about a man. His name was Bond. James Bond." The credits roll, accompanied by "We have all the time in the world" by Louis Armstrong.