Luke meets Rey, he tells her how the force brought her to him. Her parents were scared of her abilities. She is told after a couple scenes that she was born out of necessity that this balance will continue forever with the force, since the beginning all the way to his dad and now her. Luke trains her but tells her after Snoke is defeated, they will cease to fight and will not continue the Jedi order. They have a meditation scene together where she literally walks through a beam of light and she can control everything around her. She can change shapes and warp everything around her. Luke tells her she will be even more powerful than Yoda and she says who? (this got some chuckles). She also battles a creature that Luke claims is filled with evil intent and has been threatening the porgs, creatures more in tune with the force than even himself (think penguins on crack). She defeats this creature only to see it become a ghost of Anakin. Basically, Luke has tried to push her emotionally in every direction on the island in order to wake her full potential quickly. He wants Snoke gone now. It's made clear that Luke is not happy with what Snoke did to Ben and will do anything to make Rey become stronger quickly to destroy him. We get a flashback with Anakin at Luke's school and everything is destroyed. Luke sees young Ben and says "I don't want to kill you...but your life is in my hands now". We learn later Luke knew someone else would come along to balance things out with Ben so he left to get answers as to why the Jedi always fail. He used the force to shut R2 down until this person was found. Rey confronts Luke about his feelings towards the Jedi, his abandonment of his friends and everything that's happened and they don't come to an agreement. He speaks with Yoda, she meditates.
Yoda admits she is right, that the Jedi of old were hopeful but arrogant and the dark side of the force can't be the only future. Ren spends the majority of the film with Snoke. He's more unstable and leaves to trace Vader's life in hopes that he will meet his spirit. From the way Snoke acts, he doesn't seem to care much. Also, force ghosts can be destroyed. After Finn wakes up, the entire ship they're on is destroyed. Leia asked him to go find Snoke's weakness, she's been told someone has information on how to destroy him and they've arrived at the meeting point (a new planet). No one likes Leia on this planet. Rose leaves with him because it's the last escape pod and her sister trusts Finn. Poe leaves after the ship is destroyed as well with Leia and some remaining resistance. The First Order takes prisoners. They spend most of the film on the run and meet up with Holdo who immediately butts heads with what they should do next. She wants to have an alliance with the FO, Leia thinks that's a bad idea and in the meantime, sends Poe to rescue the remaining resistance supporters. Finn goes to Snoke's home planet and finds a crypt. Very expensive looking place and a tomb that's opened. Basically, we learn Snoke has switched bodies and is actually well liked by a lot of races. No one alive has seen his original body. He's with Rose and Zenn. All of this takes place after they escaped the "affluent planet" and found the kidnapped resistance members who after these past few years have decided to join the First Order. Finn appeals to some of them but not all.
Luke eventually understands that training one person at a time might be the best way forward and thanks to Rey, that this will never end so they'll have to make their own rules going forward (Anakin told her that repressing your emotions is what leads to their downfall). There will always be someone out there more powerful, good or evil. Ben finds out the location of the island because Rey was alone meditating and he sensed her. Ben doesn't tell Snoke by the way so something is going on there.
Ben fights Rey on the island, wins. Luke destroys Ben's guards with one move (they come in to attack at once, next shot, they're all on the ground). This got a great reaction but the move itself was definitely not a typical Jedi action. Ben asks Luke why he failed and that it was his parents fault for not being there for him. Luke asks Ben what he wants and asks him to help take down Snoke, that it can lead him to a new path. Ben agrees. In shock, Rey follows them (Luke has an A wing on the island!). Honestly, the Luke/Rey stuff is way more interesting than Finn's story. This has almost turned into a weird review haha. The film ends with Luke standing before Snoke as the destroyer flies away. Rey and Kylo flew off after she attacked his ship.