I'll start by saying that I don't think Batman v Superman: Dawn of Justice (2016) is a bad movie. Director Zack Snyder has an interesting visual style (although he does like to film dark). The action is strong, the takes on the classic characters interesting, and the acting gets full marks. But it just doesn't seem to hold together.
It picks up the story up during the big fight at the end of Man of Steel. We meet some of the first responders getting killed by fallout from the Superman/Zod fight, which motivates the whole hate-and-fear Superman thing. There's even a Marvel-Civil-War-style anti-superpower legislation subplot. Later, we see Clark Kent reading about Batman's extralegal activities and decides that he is a menace.
So they start plotting to take each other down. Batman will have a harder job of it, but he has a line on some kryptonite. He plans to get it by stealing it from Lex Luthor (Jesse Eisenberg). Alfred isn't happy about this, but since he's played by Jeremy Irons, we're happy with him.
When we get to the big fight, it's almost entirely based on a misunderstanding. This is something that is always happens in comics - two superheroes meet, each decides the other is evil, fight, fight, fight. The whole thing is settled when they discover that both of their mothers are named Martha. Trace Beaulieu and Frank Coniff talk about this a lot in their Movie Sign with the Mads podcast: What would have happened if Ma Kent's name was Molly? What if Lex Luthor's mother was another Martha?
A few words on casting: I love Henry Cavill as Superman and Clark. It's cute that this version of Clark lives with Lois Lane (Amy Adams), who knows that he's Superman, because she's not blind. Ben Affleck is maybe the best Batman yet - old and beaten up but hugely powerful. (I have to admit here that I've been getting Ben Affleck and Ben Stiller mixed up. They both have the same chiseled cheeks and quirked smile, you know. I thought this Ben guy had a lot of range, from Zoolander to Daredevil. I've got them straight now.)
Jesse Eisenberg playing a Lex Luthor as a long-haired semi-articulate high-tech industry guru seems like a mistake. I want a Lex Luthor with some gravitas - a thoughtful, dignified villain, preferably bald. Eisenberg seems to be doing Zuckerberg as supervillain, or maybe he can only do this one character.
This movie famously sets up the Justice League movie by showing a few of the other heroes. In some ways, it seems to take place in the CW-DC-verse, with the metahumans, although with a different set of actors. Jason Momoa as Aquaman looks (paradoxically) awesome in his short cameo. But when Gal Gadot shows up as Wonder Woman, the movie gets a real shot of adrenaline. That might even be the big problem with this movie: When you see that kind of intensity, the rest of the movie is going to suffer.