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

In the core series

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.

In spin-off games

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 Sam's eventual 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 assisting in the rescue of Nick and his father from certain death. Nick is now the mayor of Marion Town in the present day.
Calista traveled through time via Baltoy and an alternate self in Me, Myself and Time. It was 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 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 now being 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; the changes went into effect only when Arceus remembered that Ash had rescued it in the past.
Ferris traveled through time via a portal in A Restoration Confrontation! Part 1 and Part 2. It was a case of arriving in the 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 ten 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 of the hotel, which no longer looked abandoned.
In SM125, Ash and his Torracat were accidentally sent back in time by a Celebi to when Professor Kukui was five years old. Ash's talks about Pokémon Leagues and Gyms inspired Kukui and led to him creating the Alola League in the present day.

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.