Swellow was caught as a Taillow in the episode You Never Can Taillow!. It was the leader of a flock of Taillow. It stole Max's chocolate and challenged Pikachu to a battle. In its debut episode, it was shown to be a determined battler and even though it took countless Thunderbolt attacks from Pikachu, it still kept fighting. Ash captured Taillow to prevent it getting hurt more.
Its first battle was against Nicholai and his Zigzagoon in In the Knicker of Time!, Taillow's impressive flying techniques allowed it to match Nicholai's newly caught Pokémon well. In Brave the Wave, Ash chose it to battle the Template:Type2 Gym leader Brawly's Machop, despite the type advantage, Taillow lost. Its next battle was against Drew's Roselia in Pros and Con Artists, which it again lost after being paralyzed by Stun Spore.
Taillow evolved into Swellow in the episode That's Just Swellow. It had progressed to the final round in a PokéRinger tournament. It was up against James and Jessie's Dustox, and evolved at the last second to fly to victory. Several episodes later, in Sky High Gym Battle!, Swellow defeated Winona's Swellow despite Winona's Swellow using more powerful attacks such as Aerial Ace. After this victory, Ash became determined to teach his Swellow Aerial Ace. With the help of Vladimir, Ash was able to teach Swellow the move in Lessons in Lilycove!.
In Solid as a Solrock it teamed up with Pikachu in a double battle against Tate and Liza, the two of them struggled to defeat Lunatone and Solrock until Ash ordered Pikachu to use Thunder on some thunder clouds above, the clouds spat the electricity back at Pikachu and Swellow, and what would have expectedly hurt Swellow, powered it up along with Pikachu and turned it a metallic golden color. This was called Thunder Armor. With its new power, Swellow was able to finish the match quickly. Swellow was used again against Juan in Eight Ain't Enough where it battled and defeated Juan's Whiscash in a fierce battle only to be harshly beaten by his Milotic.
In the Ever Grande Conference, Swellow battled Katie's Venomoth and Scizor in A Judgment Brawl and defeated both of the Template:Type2 Pokémon, however its winning streak was broken by Kaitie's Walrein. Then in Choose It or Lose It!, it battled Morrison's Gligar, where it drew after a long battle in the sky. In Ash's final battle in the tournament, in the episode At the End of the Fray, Swellow battled powerfully against Tyson's Hariyama and Donphan, being able to stop Donphan's Rollout attack with its talons, lift it in to the air and throw it across the battlefield. Like in Ash's battle with Katie, Swellow defeated two Pokémon and proved itself to be one of Ash's most powerful Pokémon. It finally lost to Tyson's Metagross but not until after it had done the damage it needed to do for Pikachu to defeat it later.
In Tactics Theatrics!! it battled with Corphish to battle Dome Ace Tucker, and once again Swellow and its double battle partner won.
Ash left Swellow at Professor Oak's lab when he set off for Sinnoh.
In The Semi-Final Frontier!, Swellow was brought back to Ash's team where it battled against Tobias in the semi-finals of the Lily of the Valley Conference. It used Quick Attack on Tobias's Latios; however, Latios was able to dodge it. Swellow then used Aerial Ace and flew from the sky towards Latios, coming down with great force. However, Latios used Luster Purge on Swellow, knocking it out.
Right from its debut as a Taillow, Swellow has been tough and persistent. It has been noted many times in the anime how Swellow was overly stubborn and would fight to its last breath in a battle, rather than give up. An example of Swellow’s determination was in Solid as a Solrock where Ash, knowing that Swellow would enjoy the challenge, ordered a Thunder attack on it. Swellow, determined to win their battle against Tate and Liza, took the attack and used it to win the double battle.
As Professor Oak has often stated, Pokémon take on personality traits of their Trainer's, and since Swellow was already a lot like Ash when they first met, it can be said that Ash and Swellow are very similar now, with practically the same values and beliefs.