Pete's World
Pete's World is the Doctor's name for an alternate universe and home to its own Cybermen which, the head of Cybus Industries, John Lumic had created.
Overview
Pete's World was similar, though more advanced technologically, to the Doctor's universe. At the time of the Doctor's first arrival, much of the world's technology is provided by Cybus Industries, a company run by John Lumic. This includes the Zeppelins and EarPods. (DW: Rise of the Cybermen)
The Doctor derived the name from Pete Tyler, that universe's version of Rose Tyler's father, who in her universe had died in 1987. Time apparently moved quicker in this univese than in the usual ones, so that while mere months pass between his first (DW: The Age of Steel) and second encounter with inhabitants of the parallel Earth, three years had passed on Pete's World. (DW: Doomsday)
History
The Doctor was accompanied by Rose Tyler and Mickey Smith during his first visit to Pete's World. Rose learned that, on this world her father, Pete Tyler, had not died in an automobile accident (DW: Father's Day) but was still alive and a hugely successful businessman and commercial pitchman connected with Cybus Industries. On this earth, most of the populace is "wired in" to the Cybus network via cellphone-like earpods that upload information (including a daily joke) into the user's brain. Mickey found that his parallel version, Ricky Smith, is a member of an anti-Cybus terrorist cell called the Preachers.
Rose's mother, Jackie Tyler, was a socially active diva in this world, and both she and her husband lived in a mansion. Rose learned to her chagrin that she did not exist on Pete's World, but the Tylers did name their dog Rose. (DW: Rise of the Cybermen).
It was at this time that Lumic unveiled his version of the Cybermen and tested them out in hopes of "upgrading" the human race. In the ensuing conflict, Great Britain's president is killed, as is Jackie Tyler when she is upgraded and becomes a Cyberman, and Ricky Smith. After the defeat of Lumic, Mickey chose to remain on Pete's World to take over (most) of Ricky's life, and primarily to care for his elderly parallel-grandmother. (DW: The Age of Steel)
Months later, a Torchwood 1 experiment involving a rift in London results in an unusual form of contact with what is believed at first to be "the other side" (i.e. Heaven); in fact, a rip in time and space was being opened which allowed the Pete's World Cybermen (now autonomous after the death of Lumic) to cross over and begin an invasion of Earth, with the intent to "upgrade" the human race. Unknown to Torchwood, a few Cybermen came across first and slowly began infiltrating the facility, converting Torchwood personnel.
As the invasion began, the Doctor and Rose encountered fighters from Pete's World who had travelled over to try and stop the Cybermen invasion: Rose was reunited with Mickey, while the Doctor was reacquainted with Pete Tyler and the Preachers. The Doctor made a brief visit to Pete's World during this encounter, long enough to learn that the rips in time and space caused by the movement of people and Cybermen between worlds, exacerbated by the Torchwood rift experiment, were causing catastrophic and potentially civilization-ending damage to the parallel world. It was around this time that the Doctor dubbed the parallel earth "Pete's World" after Pete Tyler. (DW: Doomsday)
During the ensuing battle (which was made more complicated by an attempt by the Cult of Skaro to revive the Dalek Empire and simultaneously battle the Cybermen), Rose, Jackie Tyler (from our universe), and Mickey were ultimately trapped on Pete's World, with no way safely back without destroying their planet. Some months later (as reckoned on Pete's World; an unknown time later in our universe) The Doctor was able to make one final tearful communication with Rose by utilizing a supernova. Afterwards, no further communication was possible. The Doctor learned that, among other things, Pete's World had its own version of Torchwood. (DW: Doomsday)
Unknown to the Doctor, Rose and others on Pete's World began to work on a dimension cannon to allow transport between the two Earths. This device was also capable of reading timelines, and revealed that they all converge on Donna Noble. During this time it was discovered that, for reasons unknown, the stars in the sky were going out (a phenomenon termed, "The Darkness"). Learning that this effect was likely affecting parallel worlds and other dimensions, and after possibly trying unsuccessfully to contact the Doctor via a video signal (DW: The Poison Sky and Midnight), Rose used the new technology to transport herself back to her original Earth on several occasions, on one occasion arriving too early (DW: Partners in Crime), and on another occasion arriving in an alternate timeline in which the Doctor had been killed (DW: Turn Left). She finally reunited with the Doctor in the "main" universe (DW: The Stolen Earth). She was soon followed by Mickey Smith and Jackie Tyler.
After defeating the Daleks, Mickey chose to remain on his original Earth, and the Doctor returned Jackie and Rose to Pete's World where he asked Rose to stay in order to look after the new Doctor. (DW: Journey's End)
Alternative versions of known people=
Pete Tyler was a successful businessman who never had any children. cyber-conversion and death, he had though he had never had any children by his wife Jackie Tyler. He ran Vitex, a subsidiary of Cybus Industries.
Ricky Smith worked with the Preachers and was a wanted criminal. The Preachers were trying to stop Cybus Industries' experiments on the poor, which were actually early attempts to make Cybermen. (DW: Rise of the Cybermen, The Age of Steel) Unfortunately, Ricky died, leaving the Preachers without a leader. Mickey, Ricky's double from the other universe, joined the Preachers, and Jake became the new leader.