The Team Rocket trio, sometimes referred to as TRio or JJM, is a trio of members of Team Rocket, consisting of Jessie, James, and Meowth.
Since making their debut in the second episode of the anime, they have since appeared in almost every single episode up until the beginning of the Best Wishes series, where they appeared less frequently. As such, they are the most prominent representation of Team Rocket as a whole in the anime.
In most of their appearances, they attempt to capture Ash's Pikachu, or any other Pokémon to give to their boss, Giovanni. However, they almost always get defeated and are blasted off with their iconic catchphrase "Looks like Team Rocket's blasting off again!" (4Kids dub) or "We're blasting off again!" (TPCi dub). Typically right after making a capture, they will recite their motto, though on some occasions they're unable to finish. This has been parodied by protagonists and even other Team Rocket members, such as Butch and Cassidy.
Since their debut, the trio is near-singlemindedly obsessed with capturing Ash's Pikachu, particularly after witnessing his power, and have relentlessly pursued Ash and his friends across the various regions of the Pokémon world to do so; though they often succeed in doing so, they never manage to hold on to Pikachu for long. To this end, they frequently develop various kinds of shockproof gadgets and machinery to do so (mechas, rubber suits, etc.). However, these gadgets are often circumvented by non-Electric attacks and abilities, which they constantly forget to account for, or simply backfire in the end.
Even though they usually only cause trouble for the main characters, they have sometimes helped them, mostly when dealing with a common enemy, as shown in The Power of One and later against Team Aqua and Team Magma. They also played a key part in the fight against Team Galactic, teaming up with Looker. They occasionally put their differences aside for personal reasons, only to later return to their thieving ways. One of the more common moments of truce is during Pokémon Contests, which Jessie had a fondness for participating in; however, Ash and his friends are unaware that it is her.
On several occasions, Jessie, James and Meowth have shown that they are not that bad and even have affection for Ash and his friends. The trio heroically sacrificed themselves to certain death in The Power of One in order to allow Ash's escape on Lugia. They also saved him from a fall in the next movie, Spell of the Unown. Whilst their justification was that in the case of the world being destroyed or Ash's death, they'd be out of show business, it is implied that this is just bluster to cover the fact that they are not bad people. In Charizard's Burning Ambition, Team Rocket kept Ash's Charizard awake as it lay in the lake, and then built a huge mecha and attacked the Charicific Valley for the sole purpose of allowing Charizard to defeat them and gain acceptance in the Valley.
Though their general incompetence in making any sort of contribution to Team Rocket didn't go well for them as Giovanni contemplated firing them in one episode (but reassigned them due to problematic developments and manpower shortages in Team Rocket) and was shown to not even remember who they were in The Thief That Keeps on Thieving!. However, due to their false reports that they alone caused Team Aqua, Team Magma, and Team Galactic to disband (as well as defeating J), Matori recommended them to Giovanni for his plans in the Unova region. The trio got promoted and soon they became more serious and less goofy, changing to their black uniforms from their original white uniforms. They focused less on capturing random Pokémon and more on the assignments that are given to them straight from headquarters. In Battling For The Love of Bug-Types! however, Matori informed them that they won't be needed for any more missions at the time. They began to worry that the boss had abandoned them. Before Matori contacted them about the situation, they have already returned to their white uniforms without being informed why. Therefore, they have returned to planning their own schemes like they did in the previous series, but often carry out their current plans in the same manner as their most recent missions and Dr. Zager frequently assists them in these schemes. They do keep some gadgets, such as jetpacks they occasionally use to retreat; they very rarely blasted off during the Best Wishes series, and maintain their recent boost in athleticism.
Meowth traveled with Ash, Iris and Cilan from Meowth's Scrafty Tactics! to Crisis from the Underground Up! after apparently messing up a mission in Nimbasa City, being fired from Team Rocket and splitting up with Jessie and James. However, in Crisis from the Underground Up! it was revealed that Meowth was never fired from Team Rocket, his travels with Ash, Iris and Cilan being part of their latest scheme. Meowth then rejoined Jessie and James.
Beginning in An Epic Defense Force!, they have made various attempts to capture Meloetta, only for it to disappear on each attempt. However, they managed to capture it in Meloetta and the Undersea Temple! and Unova's Survival Crisis! with the help of Giovanni and Dr. Zager after the former defeated Ash with his Persian. The trio capturing Meloetta was part of the plan in order for Giovanni to summon the Kami trio using the Reveal Glass. However, once Meloetta was freed from his control, Giovanni became possessed by the item's powers which made him want raging power. The Team Rocket trio temporarily switch sides in order to stop Giovanni. They did so by pushing him off a cliff, which managed to snap him out of the controlled rage. Losing Meloetta foiled their plans in capturing the Kami trio, along with interference by Ridley, Ash and the others. With Giovanni back to normal, he along with the trio, Dr. Zager and the Rocket Grunts, leave Unova and return to Kanto.
They were revealed to have returned to Unova in New Places... Familiar Faces!, with returning gags in their team. They also revealed that after the failure of their big scheme to take over Unova using the power of the legendary Pokémon had failed, they had gone back for their older style of chasing Pikachu and every other seemingly valuable Pokémon around. As a part of their return to the older style, they also started using their original motto and an enhanced version of their Meowth balloon once again. However, they seemed to retain some intent of competence by still using their jetpacks on occasions and trying to accomplish their plans in a serious way, as seen when Jessie asked for Meowth to stop singing in The Light of Floccesy Ranch!.
In Ash and N: A Clash of Ideals! and Team Plasma and the Awakening Ceremony! they were spying at Team Plasma's operation at the White Ruins, waiting for the right time to enter the scene. However, they only decided to do so after Looker found out where they were hiding in What Lies Beyond Truth and Ideals! and asked them for help. Even if they fought against Team Plasma independently of Looker's intended guidance, they still did it in order to help him (having formed a mutual alliance with him during the Diamond & Pearl series), along with defeating Team Plasma, since they had a rivalry with the organization.
From Farewell, Unova! Setting Sail for New Adventures! onwards, the trio returned completely to their previous role as comic relief, retaining only their upgraded technology from Best Wishes!.