Giovanni serves as the Head of Team Rocket in the anime, never really shown taking action in field work, but rather sends the grunts and other members for that. Jessie, James, Meowth, Butch and Cassidy along with other members, are constantly striving to please him in their actions, usually without his compliance.
In the early episodes of Pokémon, his face was hidden from view and his voice was distorted. However, this version was later dropped as the series went on to become more comical. Giovanni has only been shown once as the Gym Leader of Viridian Gym, in the episode The Battle of the Badge, facing off against Gary. In this episode he used Mewtwo, which he was controlling with a machine, against Gary's Pokémon, brutally defeating him. By the time Ash challenged the Gym, Giovanni left on account of an emergency, leaving Jessie, James and Meowth in charge. Ever since the destruction of the Gym, he had never returned to it, rather it was rebuilt and had Agatha of the Kanto Elite Four take temporary leadership of it. Giovanni in the anime series might be some sort of businessman, because he is revealed to own Pokémon Island.
He possesses knowledge of the other crime syndicates in the Hoenn, Sinnoh, and Unova regions, which are also regions that he does not have a branch of Team Rocket. Despite his dislike of Jessie, James and Meowth, he allows them to try setting up new branches (as they kept following Ash to capture his Pikachu). Upon Team Galactic's defeat, Giovanni began looking into the working of a mysterious organization in Unova as he wished to obtain artifacts there to further his plans for global domination without confronting them. Giovanni allowed Jessie, James and Meowth to do as they please in Unova, working with Dr. Zager.
Giovanni returned to spearhead Team Rocket's: Operation Tempest, a stratagem which involved caputuring Meloetta. He did just this using goggles created by Dr. Zager to see the mythical Pokémon even when she was invisible. Giovanni quickly defeats Ash and rejoins Jessie, James, Meowth and Zager. Team Rocket led Giovanni to the Abyssal Temple which they had spent a while looking for. With Ash & Pikachu captured, Giovanni uses Meloetta to summon the Reveal Glass and rise the Abyssal Temple, using Meloetta's calming song, that Team Rocket had insidiously recorded during her time with Ash. Meloetta is caused to suffer in this ceremony. The Kami trio are summoned and the Reveal Glass morphs them into their, feral, viscious Therian Formes. At Giovanni's command, they battle the resistance created by the escaped Ash, Pikachu and their friends, Iris's Dragonite leds this resistance. In the midst of a titanic battle, Ash and Pikachu confront Giovanni. Ash orders Pikachu to use Electro Ball, because Piakchu had been charged up from an earlier attack, the Electro Ball's size and power are augmented significantly. The electric attack incinerates the platform Giovanni was standing on and severes the link between the sadistic leader and the tortured Meloetta. However Giovanni loses his mind because of this, ordering the Kami trio to destroy the Unova region. Jessie, James and Meowth throw themselves at their beloved boss and succesfully save him, not only from a fatal explosion but from his insane state. Team Rocket then make a total retreat to Kanto.
Giovanni is very evil and sadistic and it is hinted that he conducts dangerous experiments with Pokemon and is behind his Team Rocket schemes in Kanto, Johto and Unova. In Mewtwo Returns he shows more sadistic and evil personality than in the anime, because he tortures Mewtwo even when Domino advises that he could use Mewtwo's power for himself and before that implies that if Mewtwo doesn't surrender he will use his clones on dangerous experiments which will kill them.
Giovanni's Mewtwo was created by Giovanni's scientists on the Cinnabar Island. It first appeared in The Battle of the Badge in Giovanni's Gym battle with Gary Oak. It's so powerful it down Gary's Arcanine and Nidoking with little effort. When Gary tried to find what out Pokémon it was, Mewtwo overloaded his Pokédex. In It's Mr. Mime Time, Mewtwo escapes from Team Rocket Headquarters, destroying it in the process.