How do spells like Conjure Fey work? I mean, are we magically kidnapping unsuspecting pixies and forcing them to fight for us? Did a green hag mysteriously disappear from her coven and find herself the unwilling ally of an adventuring party? How does a mid-level spell have such a hold on every being in an entire dimension? Do the fey mind the fact that they could get pulled away at any moment? What if beings on another plane developed a Conjure Humanoid spell or something? Hm, actually, that sounds like a neat plot hook...
But seriously, this is kinda worrying. I'm sort of afraid to summon anything now. Maybe it's not as bad as it seems, and the summoned creatures are actually just mindless fey spirits taking the forms of regular fey when we call for them? But why do they get so angry when we lose control of the creature? They must not like what the spell does. Or maybe the shapeshifting fey spirits are just always like that, and will strike out at anything like a wild animal unless controlled by magic? This raises so many questions...
There's a few different ways to do it.
I believe the 2e canon held that every time a spell like this was cast, it created a little blue gem that sped around on the plane and bumped into the creature you requested and yanked it into your little battle (I remember this because there was a semi-obscure PS monster that ate those crystals). So yeah, pretty much a kidnapping.
Sometimes summoning spells require a particular creature's True Name, and the spell just sort of represents a pool of creatures that you know the True Name of. Because you know their True Name, you can force them to do your bidding. So sort of a more specific kind of kidnapping and manipulation.
Perhaps this is why the most famous summoners have been summoners of unsavory creatures such as demons and devils! ("Listen, you can gripe about being yanked away from your home and forced to participate in my fight all you want, but you are a VROCK, and if you die here, I will be doing all the planes a favor.") Gives a particularly nasty cast to those who summon divine beings...
I believe in 3e, it was explicitly some sort of copy of the creature, so that the creature itself didn't die when the summoned effect did.
An approach that I enjoy, that makes it a bit less harsh, is that these extraplanar creatures have agreed to serve you, and you specifically, because you have access to the spell. Learning a summoning spell isn't just jotting some words down in your spellbook, it is the process of making an agreement with a group of these creatures, presumably because they want to support the heroism or villainy you're working in the world. They fey spirits you summon know you by name, and have agreed to be summoned on your behalf, and so it's not a copy or a duplicate, it's the actual fey spirits (sometimes perhaps ones that you know specifically, but more often probably just the ones that were "available" to respond to the call), who actually want to do what you say, because they trust you to use their abilities wisely and in a way they would support.
The exception, of course, are the various fiends, who are willing to serve those whose ultimate goal might not be Evil, on the chance that they can twist that goal to include or create Evil. A Vrock doesn't necessarily want to help you kill the necromancer, but it's working for Demogorgon, who sees the destruction of the necromancer as a chance to plant his own cult deep within the ruins at some later point. Which is part of why fiends don't always serve willingly, and why you should be very suspicious if one does.
I like this approach because it links the caster explicitly with other groups in the world. Someone who learns
conjure fey needs to care about what the fey think about their characters' activities if they hope to keep casting it.
Elementals in 5e are explicitly wild, sentient
forces, without a body, that the summoner forces into some form on their plane to achieve some task. Which is why
aerial servants and
invisible stalkers might do nasty things if the magic binding them breaks.
You could take the same view of other summoning abilities! Perhaps the fey you summon are just the raw ambient
stuff of the feywild that you grab and twist into some living form, for a time, creating a unique satyr or pixie or whatever each time you do it, out of raw planar material that wasn't a living, thinking thing before some wizard came along and made it happen.
Just some ideas to plant in your brain!