I noticed that the only requirement on most wands is "spellcaster" (and some, such as Wand of Magic Missiles have no requirement). So any spellcaster can use any wand that requires "spellcaster" and anyone can use a Wand of Magic Missiles? Or did I miss something.
From memory, it says that spells in magic items need to be on your spell list. I may be wrong but I know the rule is in the section before the magic items under spells in items section...
DMG pg. 135 & 136- For attunement it says if the class is a spell casting class, a monster qualifies if that monster has spell slots and uses that class's spell list.
Could an Arcane Trickster use it?
Could an Arcane Trickster use it?
The Wand of Fireballs for example. It requires attunement by a spell caster class. A cleric wouldn't be able to use it as they don't cast Fireball, it's not on their spell list. If a DM thinks any spell caster should be able to use the wand, it's their world, let it be so.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.