Battlefield Scavenger — ruling 1

You can't exert a creature unless an effect allows you to do so. Similar effects that "tap and freeze" a creature (such as that of Decision Paralysis) don't exert that creature.

Battlefield Scavenger — ruling 2

If an exerted creature is already untapped during your next untap step (most likely because it had vigilance or an effect untapped it), exert's effect preventing it from untapping expires without having done anything.

Battlefield Scavenger — ruling 3

If you gain control of another player's creature until end of turn and exert it, it will untap during that player's untap step.

Battlefield Scavenger — ruling 4

Some cards have abilities that trigger whenever you exert any creature. These abilities trigger when you exert that creature or any other creature you control.

Battlefield Scavenger — ruling 5

All cards in the Amonkhet set that let you exert a creature let you do so as you declare it as an attacking creature, as do some of the cards in the Hour of Devastation set. You can't do so later in combat, and creatures put onto the battlefield attacking can't be exerted. Any abilities that trigger on exerting an attacking creature will resolve before blockers are declared.

Battlefield Scavenger : règles, fonctionnement et interactions (MTG)

Battlefield Scavenger is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

You may exert this creature as it attacks. (It won't untap during your next untap step.) Whenever you exert a creature, you may discard a card. If you do, draw a card.

How it works : Battlefield Scavenger

Original English text — Wizards of the Coast / Scryfall

#1April 18, 2017· Wizards of the Coast
You can't exert a creature unless an effect allows you to do so. Similar effects that "tap and freeze" a creature (such as that of Decision Paralysis) don't exert that creature.
No other card is named in this ruling.
#2April 18, 2017· Wizards of the Coast
If an exerted creature is already untapped during your next untap step (most likely because it had vigilance or an effect untapped it), exert's effect preventing it from untapping expires without having done anything.
No other card is named in this ruling.
#3April 18, 2017· Wizards of the Coast
If you gain control of another player's creature until end of turn and exert it, it will untap during that player's untap step.
No other card is named in this ruling.
#4April 18, 2017· Wizards of the Coast
Some cards have abilities that trigger whenever you exert any creature. These abilities trigger when you exert that creature or any other creature you control.
No other card is named in this ruling.
#5April 18, 2017· Wizards of the Coast
All cards in the Amonkhet set that let you exert a creature let you do so as you declare it as an attacking creature, as do some of the cards in the Hour of Devastation set. You can't do so later in combat, and creatures put onto the battlefield attacking can't be exerted. Any abilities that trigger on exerting an attacking creature will resolve before blockers are declared.
No other card is named in this ruling.