Stealing is a skill you learn on Zidane's Vision, the Saboteur, and it works on any enemy that can be fought normally. What is stealable is large: 41 pieces of gear that no shop, chest, quest or drop gives, plus 14 bosses that can be robbed.

FINAL FANTASY RESONANCE steal guide setup

Zidane's Vision kit for theft is:

AbilityRankAPEffect
StealMR 115Takes an item from the target
MugMR 520Steals and deals damage at the same time
Discerning EyeAwakening 120Shows what the target is carrying
Treasure HunterAwakening 350Guarantees a rare item when Steal succeeds
ThieveryBase passive30Raises damage dealt by up to 50%, scaling with how many times Steal has been used

Two rules from the game decide the setup. The abilities of the Vision you wear work without taking AP, so Discerning Eye, Treasure Hunter and Thievery only need Zidane on the hero, while Steal and Mug come from his Mastery Rank and must be equipped one by one with their AP cost. They stay equippable under another Vision, so a hero can carry Zidane's theft abilities while wearing someone else's Vision. Zidane's Sanctum is on Dirnado.

The gloves decide how often it works. The Brigand's Gloves cost 4,000 gil in the shops of the Crystal Tower and the airship and raise the success rate of Steal. The Genji Gloves are the better pair, and the reason Gilgamesh has his own storyline: he steals them in Siren's Tower in chapter 1, and the fight on the airship deck wins them back.

14 bosses can be robbed

BossWhereWhat it carries
AntlionGrandportEarth Scroll I
Cutting Edge Magitek WeaponBattlefieldPotion
Gargantuan GigantuarColosseumMist X-Ether, Magicite Cryst as the rare steal
GigantuarGronoa and PharmMist Turbo Ether, Magicite as the rare steal
GilgameshSiren's Tower and the airship deckEther, Shuriken, Mist Turbo Ether, Fuma Shuriken or Elixir as the rare steal
HexadragonCrystal TowerX-Potion, Carmine Armor as the rare steal
IntangirDragon's MawMist X-Potion, Elixir as the rare steal
Iron GiantBattlefieldPotion, Phoenix Down as the rare steal
MahadevaMysidiaMole Doll as the rare steal
No. 999Zoldaad CastleCalm Armlet
RoundwormGronoaSmoke Bomb, Angel Ring as the rare steal
SandwormZoldaadEarth Scroll II, Golem Core as the rare steal
Test Subject No. 9Zoldaad CastleMage's Shard
The Hunger v5Zoldaad CastleEarrings

The Angel Ring and the Carmine Armor have no other source in the game. Many bosses are fought only once, so equip Steal before the fight rather than after it. The rest of the optional fights are on the optional bosses page.

Magicite is a stealable drop

The cactuar family carries magicite as its rare steal: a Magicite Shard from Cactuar, which lives on Dirnado, Gronoa and two more places on the world map, a Magicite from Gigantuar on Gronoa and Pharm, and a Magicite Cryst from Gargantuan Gigantuar in the Colosseum. With Treasure Hunter on, every successful Steal on them is a piece of magicite. Every other source of magicite is on the magicite page.

The rest of the loot

The three golden shells exist to be sold: Small Golden Shell for 2,500 gil, Golden Shell for 5,000 and Large Golden Shell for 10,000. Gil itself can be stolen too, with Vaan's Vision — Gil Farmer at Mastery Rank 1 for 10 AP, Gil Farmer on Stagger at Mastery Rank 3 for 25 AP, which triggers on every stagger the hero lands, and One for the Road at Awakening 3 for 30 AP, which gives his own skills a 50% chance to do the same. A gil steal succeeds two times in three.

The game does not show item steal or drop rates. What each enemy carries is listed in its Libra entry in the in-game bestiary, so check before you fight something you cannot come back to. Treasure Hunter guarantees a rare item when Steal succeeds, and its wording only covers Steal — Mug is the way to steal while you are also doing damage.