Does Leyline of the Void prevent cards from going to the graveyard or exile them as a replacement effect?

Leyline of the Void reads: 'If a card would be put into an opponent's graveyard from anywhere, exile it instead.' This is a classic replacement effect under CR 614.1d. Rather than preventing the card from moving, it substitutes the destination: the card never actually touches the graveyard — it goes straight to exile.

Because it is a replacement effect and not a triggered ability, there is no window between the card leaving its previous zone and it landing in exile. The card is never 'in' the graveyard at any point, which means abilities that trigger 'when a card is put into a graveyard' (such as threshold or aristocrat-style triggers) will not trigger for your opponents' cards while Leyline is in play (CR 614.6).

This also means cards with 'dies' triggers (which look for 'put into a graveyard from the battlefield') will not trigger for an opponent's creatures, since the creature is exiled instead — the event 'goes to the graveyard' never occurs (CR 700.4).

Example: Your opponent's Llanowar Elves is destroyed. Normally it would go to their graveyard and trigger any 'dies' payoffs. With Leyline of the Void on the battlefield, the Elves are instead exiled, no graveyard zone is visited, and no 'dies' triggers fire.

Note that Leyline of the Void only affects opponents' cards — your own cards still go to your graveyard normally. Also, if multiple replacement effects apply to the same event, the affected player (or controller of the affected card) chooses the order they apply (CR 616.1).