Lets say a creature is attacked by an adventurer with a net.
Can the creature free themselves from the net with misty step?
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No, they cannot.
Misty Step says:
you teleport up to 30 feet to an unoccupied space that you can see.
While this doesnt say anything about clothing and equipment, that is typically assumed, as is logical (who would use this spell otherwise?).
So at least any object on you at the time of casting should not be left behind, which would include a net.
Assuming you apply unofficial Jeremy Crawford tweets, you could Misty Step out of bonds that are affixed to a surface, but a net is not, so it should still teleport with you.
Jeremy Crawford: It's up to the DM. I'd say you could teleport out of bonds that are fixed to a wall or the like.