Before the loop:
This part introduces all of the candidates for the throne. The royal linage has been interrupted by deaths and those chosen by the dragon crest must compete to be the next King/Queen
Five candidates are chosen by the Dragon, Emilia being one of them.
All five women play very important role in the story, and each has their own champion.
Because of Subaru's reckless behavior, Emilia tells him to stay put at the inn, and he promises he will.
Emilia is a girl who holds promises very seriously because she' s a spirit/elemental contractor. Promises are very important to these existences and she considers them basically absolute.
But he betrays Emilia's trust by breaking the promise by getting Apple Merchant and Rom's help sneaking into the palace.
Subaru didn't really have a plan and he gets found by Priscilla immediately. He still gets a ticket into the meeting because Priscilla was bored and wanted some entertainment.
Now he makes a fool of himself in front of the entire royal court.
He declares himself as Emilia's knight because all the other candidates have one and Emilia doesn't. Of course no one takes him seriously and Emilia herself doesn't approve him to be.
This eventually leads to Julius challenging him to a duel to quickly put Subaru in his place, granted some of the other knights don't really approve because Subaru is a complete amateur and Julius isn't, but Subaru accepts anyway.
So Subaru spends his time getting his ass beat for a surprisingly long time because if there's one thing Subaru has, it's tenacity and he just keeps getting up despite being a bloodied mess who clearly shouldn't be up.
Reinhart tries to stop the duel when he saw Subaru beat up, but Al got in his way, because he felt the fight should continue until Subaru stops.
At this point the onlookers have basically all gone silent because it's just hard to watch at this point but Subaru is insistent on getting a hit on the smug ****er, so he uses his Shakma ability (Subaru's mana gate is still very unstable and damaged at this point in time and he isn't supposed to be doing magic things so this is a stupid move no matter how you look at it).
In the end he never gets a hit in. This results in him getting the cold shoulder from Emilia and being left behind in the capital with Rem for treatment on his wounds and mana gate.
The loop starts:
He loses trust with everyone including Emilia, and they leave him in the capital.
He sinks into depression, but the only person who didn't leave his side is Rem, who displayed her unyielding love by continually caring for him.
He trains under Wilhelm, who is under Cruche's (one of the candidates) orders. He learns that the Roswall's mansion is in danger, and hurries out to get back to Emilia, breaking yet another promise.
But the road back to the mansion is hazardous due to appearance of the White Whale of Gluttony.
In his attempt to get back to the mansion he and Rem are captured by the Cult of the Witch, an evil cult who worship Satella the Witch of Envy, and schemes to bring the Witch back into the world.
Here's where the hell starts - Subaru and Rem are killed in a variety of ways, and each loop is more taxing on Subaru than the last.
In one of the loops Subaru finds his way back to the mansion alone, only to find the whole village piled in a mountain of corpses, Ram mutilated in front of them, Emilia dead in the mansion, and an enraged Puck going out of control, freezing the entire region and instantly killing Subaru.
In another loop Subaru is driven insane from the torture he receives from Betelgeuse, who rips apart Rem in front of his eyes piece by piece.
This insanity lasts a whole loop as Rem tries to carry Subaru who has turned into a drooling madman and make back to the mansion. At the end of this loop, the two are again captured and tortured, but this manages to snap Subaru back to sanity thanks to his anger.
After many deaths and revelations Subaru starts to formulate plans to save everything. He works to redeem himself in the eyes of everyone who shunned him.
He eventually wins the trust of several Queen candidates, and forms an alliance with Julius, the knight he lost duel to, Wilhelm, an elderly swordsman under Cruche, and beastmen mercenaries working for Anastasia (another candidate).
The group heads out first to destroy the White Whale who is blocking the passage to the mansion (~30 chapters dedicated to this). Wilhelm has a beef with the said Whale, for losing his wife many years ago.
The battle is very fierce and those who were eaten by the whale are ERASED from the world. History, memory of them, everything. No one, not even family, remembers them from ever existing. However, for some reason Subaru can remember them.
But after several deaths and loops, the group finally downs the whale.
Subaru's save point is moved (it seems killing the whale was an objective).
Now Subaru heads the allies to face Betelgeuse and the Cult of the Witch.
They lose several times, and everyone killed, but each time Subaru learns more about the Bishop and plans his tactics. The insane Bishop has the power to manifest invisible "Hands of God" that can kill anyone without them ever seeing them.
After many bloody battles, Subaru and his allies is victorious and Betelgeuse is killed.
It's the best possible outcome, or so it seemed.
Subaru wins back the trust of Emilia, but learns a shocking truth... she doesn't remember who Rem is.
He rushes to go see Rem, to find her comatose and no one remembering her.
Rem and Cruche has been attacked by Bishop of Gluttony. Rem was eaten and "erased" from the world, whereas Cruche's own memory was lost (others remember her fine).
Not even Ram, Rem's own sister, remembers who she is.
Rem was the only person that stayed at his side with unwavering trust and devotion, so this devastates Subaru who had just managed to recover from so much averted tragedies.
Moreover, after becoming romantically involved with Rem, Subaru despairs and commits suicide.
But when he wakes up, he realizes the "save point" had moved forward after defeating Betelgeuse, the Bishop of Sloth, and since Rem was attacked before that time, it was now impossible to go back in time to save Rem.
So many revelations about this world, Subaru's curse, and the secrets of the Witches are revealed or hinted in this arc.
But in the end of it all, it still only results in sadness.
Extra Notes:
1) At one point in arc 3, Subaru can't take the suffering anymore and decides to forget everything and run away with Rem.
He soon changes his mind, but this alternate continuity is a "what if he didn't change his mind and did run away...?"
They live happily ever after with two children.
2) Rem brings up how she loves Subaru and wants to be with him, and due to her amazing support during the ordeal, he seriously considers it but tells her he still prioritizes Emilia.
Rem is alright with this and will do her best to convince to take them both, and of course Subaru will give it a shot but will abide by whatever Emilia decides on.
So once the fight is over and everything's peachy, he brings it up to Emilia on their way to rendezvous with others including Rem.
Except Emilia has no idea who this Rem girl is, and no one else does either, and he later finds her in a coma with no one else knowing who she even is either.
The first time Subaru sees Rem in coma, he kills himself immediately. He resurrects pretty much right before that point, and this is when he realizes he cannot go back in time to save Rem anymore.
3) Due to Beatrice being in a different dimension at the time, her memories of Rem aren't taken away.
However, once she stops staying in the library, she does forget Gluttony's newer victims.
