Vayne is an auto-attack Marksman who excels in dishing out huge amounts of sustained damage due to her Silver Bolts ability, which deals true damage of a target's % maximum health. She is also great at chasing opponents with her passive ability, Nighthunter, and has decent mobility with Tumble.
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PROS

Good mobility and chasing power with Nighthunter and Tumble.
Deals true % HP damage with Silver Bolts.
Can become briefly invisible when Tumbling under the effect of Final Hour, which can be used to reposition.
Can escape opponents with Condemn and Tumble.
One of the most powerful late game hyper-carries.
One of the few marksmen who can actually jungle.

CONS

Has a weak early game.
Only does high damage on a single target at a time.
Tumble can be misused, putting Vayne in a very dangerous spot in teamfights.