Luís Alcázar arrived in Port Charles in July 2002 with the specific mission of getting rid of Sonny Corinthos and Jasper Jacks. He hired Roy DiLucca to help him, although Roy wasn't always willing. Alcázar blew up Sonny's warehouse, killing Kristina Cassadine, Alexis Davis' sister. Then he had Roy steal some important maps to Jax's family oil wells. Sonny couldn't figure out why Alcázar would be after him. Soon it was revealed that Alcázar had Brenda Barrett, the past love interest of both Sonny and Jax, held captive on board his yacht. Alcázar had rescued her 4 years ago after her accident. When Brenda heard Alcázar tell Roy to kill Sonny, Brenda made her escape so that she could warn Sonny.
After Alcázar kidnapped the children of Felicia Jones, Roy's then-girlfriend, and then kidnapped Felicia, Roy agreed to kill Sonny. But what Alcázar didn't know was that Roy and Sonny had cooked up a plan to fake Sonny's death by Roy's hand. Alcázar believed Sonny to be dead, so he moved on to getting rid of Jax next. He told Roy to follow Jax and keep Brenda away from him if she showed up. But Alcázar grew impatient and told Roy to kill Jax. When Roy balked at the idea, Alcázar decided to do it himself. He went to the church where Jax was marrying Skye Chandler-Quartermaine and attempted to shoot Jax. But Brenda showed up in time to distract him.
Roy confronted Alcázar later and they struggled. Alcázar got shot in the stomach in the process. He had Monica Quartermaine kidnapped and brought to his hiding place to save him. Although wounded, Alcázar was still obsessed with Brenda and his mission to destroy her former lovers. He figured out where she was probably hiding, her old cottage. He went there and confronted Jax, shooting him in the stomach. But before he could finish him off, Sonny showed up and shot Alcázar. Alcázar was then put on trial for killing Kristina and for trying to kill Sonny, Jax, and Zander Smith, but the charges were dropped because he has friends in high places.
Still obsessed with Brenda, Alcázar tried to gain access to her again. He even tried to enlist the help of Carly Benson, and then Jax in his task. However, it was ultimately Skye who helped him get Brenda. She had discovered that Brenda wasn't really dying. Alcázar had paid off her doctors to tell her that she was sick so that she wouldn't want to leave him and return to Port Charles. He then made Brenda take 'medicine' for her illness, effectively keeping her subdued and his captive. Skye agreed to help Alcázar get Brenda out of Port Charles because she's afraid Brenda would try to get Jax back. With Skye's help, Alcázar kidnapped Brenda and got on a jet headed for South America with her. But Sonny heard about it in time to get on the plane as well.
The plane crash landed in a Caribbean jungle. Alcázar hid out and ordered his associates to kill Sonny while they were on the island. Sonny found him and tied him up. Before Sonny could kill him, Brenda grabbed the gun and tried to do it herself. Alcázar escaped and set off an explosion. While Sonny and Alcázar struggled, Jason Morgan and Carly showed up. They restrained Alcázar and headed back to Port Charles.
Once back in Port Charles, Alcázar ran into Alexis at the hospital and taunted her over not being convicted of her sister's murder. Alexis threatened to kill him. They met again later outside, and while arguing, Alexis went into premature labor. She begged Alcázar to help her, but he just walked away.
Sonny threatened to have Alcázar killed, and Marcus Taggert said that if anything happened to Alcázar, he would come after Sonny. Jason and Sonny discussed how to kill Alcázar without implicating Sonny. Alcázar visited Alexis in the neonatal ICU and Alexis attacked him. Later, Alcázar crashed a party at the Quartermaine mansion given in Brenda's honor. He told her he still wanted her, but she told him off and threatened to kill him if he didn't leave her alone. He left with Skye in his limo, driven by Jason.
Back at his hotel room, he slept with a very drunk Skye who passed out afterwards. Jason was making moves to kill Alcázar that night, but Sonny called it off because A.J. Quartermaine seemed to suspect something. Brenda went to see Alcázar and struggled with him, wounding him with a knife she found. She left without killing him. Someone else paid him a visit, which ended with Alcázar falling over the railing of his balcony to his death 14 stories below.
Several people had threatened to kill Alcázar, but Jason and Brenda ended up being the one's put on trial, with Alexis defending them. At the last minute, the real killer called with evidence that cleared them. After weeks of memory loss due to her severe inebriation at the time, Skye remembered seeing the real killer in Alcázar's room. It was Alexis, who was suffering from a mental illness known as dissociative identity disorder, which prevented her from being sent to prison. Alexis was actually faking her mental illness, but she played the system to get away with murder.