Time travel

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Time travel is an infrequent theme in the Pokémon franchise and has been depicted in several canons, including the games, the anime, and various manga. In general, stories in which a character travels through time focus on the repercussions of traveling into the past or the future. Usually, the motivation for time traveling comes from the need or desire to change history. Characters who interfere with the timeline will generally notice an altered present upon their return.

Ash, Dawn, Brock, and Sheena traveling trough time in the anime

Two notable Pokémon possess time travel abilities. These are the Mythical Celebi, which is known as the Time Travel Pokémon and has been shown to physically travel into different time periods, and the Legendary Dialga, the Temporal Pokémon that can travel at will through past and future and has the power to send humans and Pokémon to specific points in time.

In the games

The Time Capsule is said to send Pokémon back and forth through time to explain how trading works between Generation I and II games.
The player travels through time via Celebi in HeartGold and SoulSilver. The objective is to battle Giovanni in the past, as well as discovering part of Silver's past.
In Black 2 and White 2, one of Pokéstar Studios's film series is about time-traveling to the future.
The plots of Pokémon Mystery Dungeon: Explorers of Time and Explorers of Darkness and Explorers of Sky heavily involve around time-traveling in the Pokémon world.
The multiplayer missions of Pokémon Ranger: Guardian Signs take place in various temples in the past of Cocona Village.

In the anime

Sam was sent 40 years into the future after meeting Celebi in Celebi: The Voice of the Forest. There, he encountered Ash and his friends. It is unknown if the events in the future and return to the past directly altered the original timeline, but it is hinted that it might not have and these events were already present in the original timeline.
Ritchie was sent into the past via Celebi in Celebi and Joy!. Events in the past directly altered the original timeline, with Ritchie helping to rescue Nick and his father from dying. Nick is now Marion Town's modern day mayor.
Calista traveled through time via Baltoy and an alter in Me, Myself and Time. It's also a case of meeting one's younger self. It is unknown if the events in the past directly alter the original timeline.
May, her Squirtle and Meowth traveled through time with via Edna's locket in Time Warp Heals All Wounds. Events in the past directly altered the original timeline, including the continued service of the Fuchsia City train station and Jonathan was now alive.
Ash, Dawn, Brock, and Sheena traveled through time via Dialga in Arceus and the Jewel of Life. Events in the past affected the original timeline, though not immediately, only when Arceus remembered that Ash had rescued it in the past.
Ferris traveled through time via a portal in the episode arc, A Restoration Confrontation! Part 1 and Part Two. It is also a case of arriving in the far distant past as opposed to the recent past. It is unknown if the events in the past directly altered the original timeline.
Ash, Serena, Clemont, and Bonnie traveled 10 years into the past via Rotom and an elevator in Rotom's Wish!. Events in the past directly altered the original timeline. Weston had originally lost his battle and the ownership of the Lost Hotel to Mantle, but the group revised this and Weston was now in-charge and the hotel no longer looked abandoned.
In SM125 Ash and his Torracat were sent back in time by a Celebi to when Professor Kukui was five years old. The impact of Kukui own ambitions following his battle with Ash and their later discussion about the Pokémon League is currently unclear.

In the manga

In the Pokémon Adventures manga

The Masked Man desired Celebi's time-traveling ability to reunite himself with his two dead Pokémon. He wound up disappearing into Celebi's time vortex.
Ruby's Celebi would later alter the events of the final battle, reviving both Norman and Steven who had died during the battle in the fourth chapter and Courtney who died in the third.

In the Pokémon Gold & Silver: The Golden Boys manga

Eusine used Bill's Time Capsule to send his Pikachu to the past, where it became friends with Gold. Later, when the appearance of the Black Tyranitar threatened to alter the future, Pikachu almost vanished.

In the Pokémon Pocket Monsters manga

Red and his Pokémon time traveled in The Ancient Pokémon Discovery!, Find the Legendary Pokémon!!, and PMDP27.