HOPE
This is not just about Superman, whose suit’s S meant “hope” on his already destroyed home planet, Krypton. It’s also present in all the other character arcs, and because of that, it's the most important theme out of all. Clark Kent/Superman tries to get closer to humanity, but at the same time he’s affected by those who criticize him because of his abilities. Lois and Martha are the two people he loves the most and they’re the ones that inspire him every day. At one point he lost his self-confidence as a hero and as someone who wants to help others, taking the blame on his shoulders for things he didn't do in the first place. But it was thanks to what he'd learned from his adoptive father, Jonathan Kent, that he didn't give up. Superman gave people hope whenever he was around to save them from danger. But when he died, they cried for him and they built a monument honoring him, which referenced a quote from Sir Christopher Wren. There are also very, very subtle references to Joseph Campbell, that you would only find out about with the help of some interviews with the filmmakers. The more you analyse the story, the more you realise how much Batman v Superman: Dawn of Justice borrowed from Campbell's philosophy about the hero's path. Going back to Man of Steel, we see that Jonathan doesn't want his son to be rejected by the world, but his very dream is that Clark one day becomes the Superman that we know and love from the comics, the one that people root for all the time. However, he doesn't see it happening because we live in a very distrustful and paranoid world. And the truth is that we don't deserve a Superman, but we need one. We need someone who becomes the light to shine the way. And Clark eventually becomes that when he dies. We, as human beings, usually don't appreciate the things around us up until they are gone. That's what eventually happens once Superman is gone.
Bruce Wayne's/Batman's arc is about redemption. He is the exact opposite of Clark Kent because aside from Alfred, the people he cared about are dead. He feels broken inside, he’s more careless, and even considers himself a criminal. After the events in Man of steel, his ultimate goal is to destroy Superman. He feels that doing it so is not only his duty and responsibility, but also his legacy for humanity. But at the end of Batman v Superman: Dawn of Justice, he discovered that Superman was more human than he had ever been and that he would've turned into Joe Chill, the man who killed Thomas and Martha Wayne, if he had let Martha Kent die. It was Clark's actions that brought back Bruce’s hope that there's still good in mankind.
Lex Luthor, however, is a lost cause because he believes someone with so much power, such as Superman, should not be considered a hero, and because he sees humanity just as a tool for his plans. He’s mentally unstable and full of rage. Those two elements lead to him being playful, socially awkward and a total psychopath at the same time.
Then we have Lois Lane, Diana Prince, and the whole world. Lois is 100% sure that Superman is not a bad person in the slightest and she's willing to do what's necessary to prove it. Diana told Bruce that she had lost her faith in the human race and that she had eventually stayed away from it during a time of hatred and suffering (most probably, World War I).
In regards to the characters, I’m going to focus on Superman, Lex Luthor and Batman. Superman has extraordinary abilities, but his greatest power is his will to do the right thing. Lex has three characteristics that are also his greatest weapons: being a business man, a manipulator and a criminal master mind. He’s the one who pulled the strings for Batman and Superman to fight. He forced Superman to kill Batman or otherwise, Martha Kent would die. He got access to the Scout Ship, Zod’s corpse and kryptonite. He's learned about other worlds, such as Krypton and possibly Apokolips (Darkseid), and he created Doomsday in order to kill the man of steel, kind of like when he created Bizarro in the comics. Lex also philosophizes about the meaning of power, gods and devils. Batman has been fighting crime for twenty years, but it seems like he's more brutal than ever, whether it's branding the worst of the worst criminals to strike fear and warn them to think twice before they commit a crime, breaking bones, or straight up killing people. And just when he's threatening Lex with the burning brand, he decides not to brand him because he's trying to become a better person.
SACRIFICE AND HEROISM
Sacrifice is part of being a hero, and we see a lot of that through several characters:
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Thomas Wayne tried to protect his family, but failed at it.
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Bruce Wayne did everything he could during the destruction of Metropolis, but still, thousands of people died. After understanding that everything was planned by Lex, Batman promised Superman that Martha would not die. So he went to the ware house that Martha was in, fought everyone in there and saved her. He did all that for someone he had never met before. This shows not only that he's redeeming himself from his blinded hatred towards Superman, but also from his feeling of powerlessness, his feeling of not having been able to do anything when his parents got shot. He also risked his life distracting Doomsday, so that the latter one would follow him to an unpopulated area in Gotham.
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Superman's arc in this movie as a whole reflected a lot of what Joseph Campbell talked about in his book "The Hero with a Thousand Faces". He acted heroically throughout most of the film. He was constantly saving people around the world. Unfortunately, that didn’t stop everyone from criticising him and questioning his existence. He carried the victims of the bombing of the US Capitol to the ambulances. He saved the love of his life, Lois Lane, a few times. He went where Batman was waiting for him because all he wanted was to save his mother. He also saved Lex, the one who planned everything to destroy him, from Doomsday’s fist. And finally, Superman made the ultimate sacrifice by killing the kryptonian creature with the same weapon that almost killed him in the first place. While he succeeded in doing it, Doomsday in return stabbed the man of steel with one of his spikes. That act of heroism by Superman is what inspired Batman to be a better person, as well as many others.
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Lois Lane unmasked Lex Luthor and revealed to the public all of his crimes. It was thanks to her that Batman didn’t kill Superman. And while she made a mistake by throwing the spear to the water, she still tried to help by getting it back.
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Wonder Woman saved Batman from Doomsday’s heat vision and stayed there to help both him and Superman stop the monster.
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In the scene where Clark was walking through the mountains, he had a vision of Jonathan Kent, who told him a tragic story about how he had saved his farm and had then been rewarded with a "hero cake", but had accidentally messed up the Lang's farm in the process. Then, Jonathan said that this had given him nightmares for a very long time up until he had met Martha. And because of her, he had restored his faith in the world.
FAMILY
Part of what drove the three main characters (Bruce, Clark and Lex) to do what they did has something to do with their families.
Clark still has his mom and he has moved to the next level with Lois. Both women are the two people he can count on for anything. We also see how much Clark misses Jonathan and that he values everything he´s learned from him.
Bruce was severely scarred by the death of his parents and he constantly visits their grave house. When Batman was about to kill Superman, the latter one screamed “Save Martha!”. That affected Bruce Wayne emotionally and brought him back a lot of memories about his mother. At that moment, he mirrored himself in Clark, remembering that night that had changed him as a kid forever. The love between a mother and a son is unconditional, and it’s what made Batman and Superman reconcile with each other, and united them at the end. As for Alfred, he’s more of an older friend than a father figure this time.
Going back to Lex being unredeemable, part of that is due the rough childhood he had. When he met Superman at the top of the Lexcorp building, he mentioned how much he had suffered as a child because of his father’s cruelties. Speaking of Lex Luthor Senior, he gave his son Lexcorp Industries at a very young age, and Junior eventually modernized it and turned it into an incredibly advanced high tech company. He also displays an obsession with the way his father left his private office before he "supposedly" died. It's also a nice parallel that Lex, Clark and Bruce lost their fathers.
In addition, we have the Daily Planet, in which the boss, Perry White is more or less a paternal figure and all his employees his children. Lois would be his favorite daughter, whereas Clark would be that rebellious son that wants to do something different from what his parents have told him to do, and is always having an arguing with them (in this case, Perry).
JUSTICE
The subtitle "Dawn of Justice" isn't just a tease for the eventual Justice League movie, it is also the second most important theme right behind hope because Batman v Superman: Dawn of Justice is a film that explores the injustices of today's world. The lies developed by Lex Luthor to make Superman and Batman look dangerous, the mistrust from some citizens towards both heroes and the questioning of their methods are what to lead to a constant debate about them. Clark Kent investigates the caped crusader and comes to the conclusion that the vigilante needs to be stopped. Unfortunately, the police doesn’t do anything about it. Perry White is always reminding him that as time had changed, the way of thinking in America had as well, which is a reflection to how America is today. Lois Lane is searching for the truth behind the events in Africa through a bullet that got stacked in her notebook. Bruce Wayne is doing what he thinks is the right thing when it comes to the man of steel. Justice is essential in politics in both the objective and subjective ways and Senator Finch is always talking about what democracy means.
In the third act of the film, Batman and Superman put their differences aside to fight together against evil forces, and Wonder Woman joins them. Lex has faked his insanity so that he wouldn't have to worry about trials. But Batman brings him to justice by transferring him to Arkham Asylum. Batman v Superman: Dawn of Justice was a divisive movie. Some people loved it and some people hated it. It is a film in which there's a lot going on, but at the end of the day, it's "THE DAWN OF THE JUSTICE LEAGUE".