If a card is discarded while Rest in Peace is on the battlefield, abilities that function when a card is discarded (such as madness) still work, even though that card never reaches a graveyard. In addition, spells or abilities that check the characteristics of a discarded card (such as Chandra Ablaze's first ability) can find that card in exile.

While Rest in Peace is on the battlefield, abilities that trigger whenever a creature dies won't trigger because cards and tokens are never put into a player's graveyard.

If Rest in Peace is destroyed by a spell, Rest in Peace will be exiled and then the spell will be put into its owner's graveyard.