Story

Throughout the Portal series, you take on the role of Chell, a young woman trapped within the Aperture Science complex. Chell is forced to solve tests of varying difficulty in chambers designed by an AI-gone-rogue named GLaDOS. During the early stages of the testing, Chell is granted usage of the Handheld Portal Device (commonly referred to as the Portal Gun), a piece of equipment developed by Aperture Science that allows Chell to create portals that act as gates between each other, allowing Chell to quickly traverse areas or reach normally unreachable places.

Portal
Portal has two distinct parts, the test chambers and the escape.

Act 1: The Test Chambers
The game begins with Chell awakening in a Relaxation Vault, where she is briefed by the voice of GLaDOS coming from speakers, before being released through a portal. The player is introduced to the testing process and mechanics, shortly thereafter obtaining the Handheld Portal Gun. As Chell makes her way through test chambers it becomes clear Motivating Chell with the promise of Cake at the end of the testing, Chell is put through tests of increasing complexity.

Portal: Still Alive
Portal: Still Alive is a Xbox 360 Live Arcade port of Portal, containing additional content in the form of new advanced chambers, inspired by Portal: The Flash version, with no additional story material.

Portal 2: Lab Rat
The Lab Rat comic bridges the gap between Portal and Portal 2, which introduces us to Doug Rattmann, a scientist at Aperture Science

Part 1
Part 1 follows Doug Rattmann as he is tracking Chell through the Enrichment Center. He is having a monologue about reality and how the mind sees it, and is shown to be psychotic, forced to take ziprasidone [sic] to curb the effects of his schizophrenia. Through the story, he carries a Companion Cube that he hears talking to him and giving him advice. The main story is also intersected with flashbacks of the period during which GLaDOS was still being built, showing Rattmann's involvement in the project.

Soon after discovering Chell, it appears he has not taken his medication for a while, and he takes his two final pills, against the Companion Cube's advice not to take them. A first flashback is shown, with a younger Rattmann overhearing two colleagues saying they put cameras in the cameras, something that an unidentified person is not to suspect. While he runs through the facility and makes another mural, Chell reaches Test Chamber 19,

Then another flashback set in GLaDOS' chamber is shown. There Rattmann is seen working with his colleague Henry, who compares their breakthrough with GLaDOS to Einstein discovering relativity and NASA reaching the Moon. Rattmann expresses his doubts about GLaDOS' reliability,

Back to reality,

Then a third flashback has Henry showing Rattmann the newly designed Morality Core,

Again back to reality, the Cube tells Rattmann to run away while he is outside, but feeling he is responsible for the whole mess, he prefers to get back inside,

Part 2
Part 2 opens with Doug Rattmann traversing the innards of the facility. The Companion Cube informs him that the anti-psychotic he took in Part 1 is starting to work, as the Cube slowly fades to silence.

Time for another flashback, this time set after Rattmann,  is taunted by GLaDOS about his schizophrenia as he escapes from the main testing facility. While GLaDOS continues to taunt and manipulate him, Rattmann manages to reach the file room where he finds

Back to reality, Rattmann is lying on the floor, wounded by the Turrets, reaches out to his Companion Cube but loses consciousness.

Another flashback begins, involving Henry having a conversation with GLaDOS. During the conversation, she tells him she would like to perform a recreation of the Schrödinger's cat experiment during "Bring Your Cat to Work Day". She says that, added to the boxes and the cats, she needs a little neurotoxin. Henry, accepts, "as long as it's for science",

Doug regains consciousness, and his schizophrenia has returned. The Cube can talk again and asks about to which he admits it was just a hunch. The Cube then tells Doug to

Exhausted, Rattmann crawls into the bed of a Relaxation Vault, and presumably falls asleep. It was later revealed by Valve that Rattmann

Trivia

 * In order to flesh out the story in Portal 2, Valve originally intended to include an exhibition within the Aperture Science facility, one composed of different dioramas showcasing various aspects of the company and its philosophy. The dioramas were ultimately cut before the final release.