Stardust

Stardust is a consumable, Pokémon-related resource that can be used by trainers to strengthen their Pokémon or perform trading. The amount of received Stardust in 30 minutes can be increased by 50% with the usage of a Star Piece.

Pokémon power up
The amount of Stardust required to power up a Pokémon is proportional to the percentage of the Pokémon's maximum potential CP. The cost of each power up can be 200 to 10,000 Stardust. The cost of powering up a Lucky Pokémon is halved.

There is no difference in the amount of Stardust required to power up a Pokémon regarding its evolution stage form. For instance, the same amount of Stardust is needed to power up Pikachu as Raichu that evolved from the same Pikachu.

Trading
Stardust is necessary to perform Pokémon trading. Pokédex unregistered, Shiny, and Legendary Pokémon require more Stardust to be traded. The amount required can be reduced by having higher friendship level with another trainer.

Second Charged Attack unlock
Stardust can be also used to unlock the second Charged Attack of Pokémon with more than one Charged Attack. Unlock cost can be 10,000, 50,000, 75,000, or 100,000 Stardust.

Purification
Stardust is necessary to purify Shadow Pokémon left by Team GO Rocket.

Stardust events
This list does not include bonuses in Mystery Bonus Hour.

Trivia

 * Stardust multipliers from concurrent events may not stack with each other, only the highest one will apply. This does stack multiplicatively with Star Piece and Weather boost, however.