Tribute

Tribute, known as Release and formerly Sacrifice in the OCG, is usually a way of voluntarily sending a card from your side of the field to the Graveyard, often used to activate a card effect or perform a Summon. When you Tribute a card it is not considered destroyed. Some examples include:
 * Monsters being Tributed for a Tribute Summon.
 * "Exiled Force" Tributing itself in order to activate its effect to destroy one monster on the field.
 * Ritual Monsters requiring their corresponding Ritual Spell Card and a Tribute of Monster Cards whose total Level is greater than or equal to the Level of the Ritual Monster in order for it to be summoned to the field.

Unless the card specifically states that you can Tribute your opponent's monsters like "Soul Exchange" or "Lava Golem", a Player can only Tribute monsters on their side of the field.

When Tributing for a card effect, the Tribute(s) are considered Costs, which means players cannot respond to the Tributes with card effects, since paying a Cost has no Spell Speed. This also means that Tributes occur before the activation of the effect that they are being Tributed for.

While Tributing a monster for a Tribute Summon is not technically considered a Cost, the Tributed monster still leaves the field before a player can respond to the action.