Andrew is the younger brother of Tucker Wells, the student of Sunnydale high that summoned and trained a pack of hellhounds to attack the senior prom. Andrew lived in his brother's shadow for a time, trying to distinguish himself as the guy who sent winged monkey demons to attack the school play (Romeo and Juliet).
Andrew joined Jonathan Levinson and Warren Mears to form "The Trio". Using their individual talents of summoning demons, magic, and advanced technology the three planned to make themselves rich as "Super Villains". While all three knew Buffy from school, their first contact with her as the Trio was when they had contracted a demon to help them rob a bank that Buffy happened to be applying for a loan at. While the three believed themselves to be Buffy's arch-nemeses, they had trouble causing more than an irritation in her life. The group accidentally turned Buffy invisible for a time, summoned a demon with toxic psychoactive quills that made her believe her life was a dream, and took turns seeing whose special skills could cause the largest disturbance in Buffy's life.
The groups ambitions rapidly turned from an annoyance to a serious threat after the death of Warren's ex-girlfriend. They attempted to pin the crime on Buffy, but she caught on when she learned it was Warren's ex. Warren's quest to destroy Buffy took the group toward its demise. During an armored car heist gone wrong, Warren had managed to escape with a jetpack, but when Andrew turned on his jetpack he flew into an awning, knocking himself unconscious. Andrew was arrested along with Jonathan. Warren returned to Buffy's house afterward with a handgun, managing to hospitalize Buffy and kill Willow's girlfriend Tara. This sent Willow into a rage where she could no longer control herself or her magic. Willow caught Warren first and ripped the skin from his body.
With Warren believed dead, Andrew and Jonathan were sprung from jail by Buffy, Xander, and Anya in order to keep them alive and away from Dark Willow. After seeing her power in person, Andrew commented that she was like Phoenix Force. Willow caught up with the group at the Magic Box where Anya was able to keep her from killing Andrew and Jonathan with a counter spell. The way he recounts the incident is quite different, and involves him simply waving off her magics and protecting Jonathan. While Buffy and Anya attempted to keep Willow busy, Andrew and Jonathan were able to escape with Xander and Dawn, and were later able to escape from Xander, leaving the group to try to disarm Willow and prevent her from destroying the world.
After slipping away from Xander and Buffy, Andrew and Jonathan took a van to Mexico as fugitives. There Andrew began seeing visions of his slain friend Warren. These visions were actually manifestations of the original evil of the world known as "The First". Believing Warren's spirit sought to make the three of them gods (which Andrew thought meant they would stroll through golden fields in white robes), Andrew located a dagger of the first's choosing and convinced Jonathan to travel back to Sunnydale with him to acquire great power. Following The First's instructions, Andrew and Jonathan unearthed an ancient seal under the new Sunnydale High and Andrew used the blade to kill Jonathan. Jonathan's blood, however, was not enough to open the seal. The First (still taking Warren's form) instructed Andrew to go get more blood in order to open the seal, and insisted that Jonathan was with him in a better place.
Warren went to the local butcher shop to get enough blood to open the seal, but was discovered by Xander and Anya who were getting blood to sustain Spike. Xander brought Andrew back to Buffy's home, where the group tied him to a chair, and Xander and Anya attempted to use a routine of "good cop, bad cop" in order to get Andrew to tell them what he knew. They were finally able to get Andrew to start talking when The First triggered a memory trigger in Spike, who burst through the wall and bit Andrew. Buffy was able to restrain Spike, and they were able to save Andrew (who they kept tied to a chair in the living room).
Andrew was touched that they saved him, and began telling stories and babbling about turning away from the Dark Side and becoming good. From the chair, Andrew continued to irritate Buffy and the gang. Andrew even (reluctantly) agreed to assist Buffy in stopping the madness in the high school caused by the Seal that Andrew helped to activate. The Seal, which was activated by blood that Andrew spilled, could only be deactivated by Andrew's tears. To get Andrew's tears Buffy made Andrew face what he did to his best friend, Jonathan, and told him that she had to kill him over the seal to stop it.
After stopping the seal, Andrew continued to stay at Buffy's house, irritating all of its many inhabitants. When The First came back to Andrew as Jonathan, Andrew even attempted to help the Scoobies by wearing a wire and attempting (quite poorly) to elicit more information about the nature of The First.
During the battle of Sunnydale, Andrew came along to help the gang. He fought alongside Anya against the Ubervamps, and Anya died protecting him. Andrew made it out of the school relatively unharmed, and got out of Sunnydale with the Scoobies and the Slayers before the town imploded.
Since the destruction of Sunnydale, Andrew has remained with the Scoobies. At first, Andrew was trained to be a Watcher by Giles and was sent to Los Angeles to supervise Angel's capture of Slayer Dana. Later, Andrew was put in charge of his own regiment of Slayers in Italy, and became one of Buffy's closer friends and most valuable Watchers and recruitment agents. He accompanies the core group on a mission to Tokyo, and later teams up with Buffy to hunt down rogue Slayer Simone Doffler.
While initially useless, Andrew is technically a genius, part of the inclusion criteria for supervillain group The Trio. His specialty, like that of his brother, was demon summoning. Later, he developed Watcher skills under the tutelage of Rupert Giles: these require familiarities with the occult, Slayer history, and some degree of fighting skills. Recently, Andrew's genius and demon-summoning expertise were shown when he managed to genetically recreate a long-extinct breed of demon through recombinant DNA experiments.